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M5-1

EXPERIMENT No: M5

Effect of Agitation on Solid Liquid Mass Transfer

Objective

The objective of this experiment is to study the dissolution of solid spherical particles

in an agitated liquid using different types of agitators and to determine experimentally

the interphase mass transfer coefficient.

Description of Equipment

A schematic diagram of the equipment is illustrated in Figure 1. The apparatus

basically consists of an agitated vessel of 28.75 cm in diameter and 40 cm in height,

sour ball solids of diameter in the range of 1.5 to 2.5 cm, distilled water as a

dissolving liquid, two type of impellers, a ladle, weighing balance, and a drain valve.

The agitated vessel is provided with a lid on the top of the tank with a slot up to the

center, which allows the shaft of impeller to pass through the lid. The lid prevents any

splashing of liquid during agitation. Four standard baffles are provided in the vessel,

which inhibit the formation of vortex during agitation.

The types of impeller are: a three-bladed 45° pitched-blade impeller and a six-bladed

high-efficiency impeller. The diameter of both impellers is 10 cm. The impeller

bottom clearance is kept one-fourth of tank diameter. The sourball solid is composed

of a mixture of sugar, citric acid, and color additives. This material is inexpensive and

safe, and its high solubility allows a number of successive experimental runs to be

made with a single liquid batch. Since the particle size and shape changes during the

experiment, the mass transfer might also change. Therefore, for the sake of simplicityit is assumed that the shape of particles and interphase mass transfer coefficient do not

change and are representative of the entire experiment.

Theoretical Background

Solid-liquid mass transfer is important in many industrial processes such as

dissolution, crystallization, solid-liquid extraction, fermentation, etc. Agitated vessels

are often used because they are effective in suspending solids particles, ensuring that

all the surface area available is utilized and because they lead to good transfer rates

[1].

The rate of mass transfer between a solid and an agitated liquid is usually described

by the following relation (1-3).

( ) LSAT LS C C Ak m −=& (1)

The experiment is conducted on a batch system, with the result that a transient mass

balance on the dissolving solid takes the form



M5-2

( ) LSAT LS C C Ak mdt

dM −−=−= & (2)

while the corresponding mass balance on the liquid phase is

( ) LSAT LS

L

L C C Ak mdt

dC V −== & (3)

These model equations are coupled through the liquid concentration term and must be

solved simultaneously. The solution procedure can be simplified by noting that the

total amount of solid distributed in the solid and liquid phases remain constant at any

instant.

M V C M V C o L Lo L L+ = + (4)

This equation can be combined with Eq. (2) and solved to yield the model predictions.

However, as the solids dissolve, they change their size and shape, and the resulting

changes in the interfacial area should be taken into account before the model

equations can be solved. In this analysis, any effect of changing particle size on the

interphase mass transfer coefficient is ignored.

The sourball solids studied in the experiment are initially spherical and are assumed

to retain their spherical shape as they dissolve. The solids are also of same initial size,

and it is assumed that all of the solids dissolve at the same rate. Under these

assumptions, the mass of the solids remaining in the solid phase at any time for a

system of n balls with radius ‘r’, is

M r ns= 4

33

π ρ (5)

the corresponding interfacial area is

A r n= 4 2π (6)

and the value of C SAT

is experimentally found to be 1613 kg/m3 at 20 °C.

Substitution of Eqs. (4), (5), and (6) into Eq. (2) yields the form of the model equationthat can be solved for the mass of candies remaining in the solid phase at any time,

dM

dt k

nM C C

M M

V LS s

SAT LOo

L

= − ⎡

⎣⎢⎤⎦⎥

− + −⎛

⎝ ⎜ ⎞

⎠⎟⎡

⎣⎢⎤⎦⎥

36 2

2

1 3π

ρ

/

(7)



M5-3

This equation can be solved numerically, but an analytical solution is possible if the

liquid phase concentration ( )C L is always much less than saturated concentration

( )C C L SAT << and can be neglected. Under these conditions, Eq. (7) can be

integrated to yield the following relation between time and the fraction of remaining

solid phase.

M

M

n

M k C t

o o s LS SAT = −

⎛ ⎝ ⎜

⎞ ⎠⎟

⎡

⎣⎢

⎤

⎦⎥1

4

3 2

1 3 3

π

ρ

/

(8)

Boon-Long (1) developed a correlation for mass transfer from suspended solids to a

liquid in agitated vessels as follows:

Sh = 0.046 Re0.283

Ga0.173

U-0.011

(T/d)0.019

Sc0.461

(9)

The above correlation is quite useful in comparing with experimental results.

Experimental Procedure

1. Close the drain valve of the agitated vessel.

2. Fill the agitated vessel with distilled water up to the mark equivalent to the

diameter of the vessel, and measure its volume.

3. Hook-up either type of impeller to the agitator assembly with the help of an

allen-key.

4. Take three sourball solids, weigh and measure their average diameter.

5. Start the agitator. Adjust the speed of impeller to 148 rpm (2 on scale) with the

help of a small wheel located on the top right hand side of the agitator, then

stop the agitator.

6. Put the solids into the vessel and start the agitator.

7. After 3 minutes of dissolution, stop the agitator and remove the balls with the

help of a ladle, dry them with a tissue paper, weigh them, and put them back

into the vessel.

8. Repeat the steps 6 and 7 for 3 to 4 times.

9. Add fresh three solids into the vessel having measured their weights and

average diameter.

10. Start the agitator and adjust the speed to 219 rpm (4 on the scale), and then

repeat steps 6 to 8.



M5-4

11. Remove the impeller and replace it with the other type of impeller.

12. Repeat steps 4 to 10 in order to obtain a new set of data for the second type of

impeller.

IMPORTANT: Do not adjust the speed of impeller while the motor of agitator isstopped.

Experimental Program

In accordance with the procedures given earlier the following will be measured and

observed:

(i) Measure the volume of the distilled water charged to the vessel, and the average

diameter & weight of solids.

(ii) Measure the loss of wt. of solids with time.

(iii) Measure the loss of wt. of solids with change in the rpm of impeller.

(iv) Measure the loss of wt. of solids by using the different types of impellers.

Data Analysis

(i) Plot a graph of (M/Mo)1/3

vs t for each of the two different types of impeller and

the two speeds using equation (8). Obtain k Ls

from these graphs.

(ii) Plot a graph of mass transfer coefficient ( )k LS vs. agitation speed (rpm) for the

two types of impeller.

(iii) Compare the k Ls (exp) with k Ls (theoretical).

REFERENCES.

1. S. Boon-Long, C. Laguerie and J.P. Coudere "Mass Transfer from suspended solids

to a liquid in Agitated Vessels", Chem. Eng. Sci., 33, p. 813 (1978).

2. Nienow, A.W., "The Mixer as a Reactor: Liquid/Solid Systems", Chapter 18 ofMixing in the Process Industries, edited by N. Harnby, M.F. Edwards, and A.W.

Nienow, Butterworths, London (1985).

3. M. Elizabeth Sensel and Kevin J. Myers, "Add some Flavor to your Agitation

Experiment", Chem. Eng. Ed., 26 (3), p. 156 (1992).

NOTATION:



M5-5

A = total liquid-solid interfacial area at any time, (m2).

C L = liquid-phase concentration of the solute, (kg/m3).

C SAT =equilibrium liquid-phase concentration of the solute, (kg/m3).

d = Particle diameter, (m).

Dν= Diffusivity of solid ball (sucrose) into water, (m2/s).

g = gravitational constant, (m/sec2).

Ga gd

= ρ

μ

2 3

2. , Gallileo number

k LS =liquid-solid interphase mass transfer coefficient, (m/s).

M = total mass of the solute (solids) remaining in the solid-phase at any time, (kg).

m& = rate of interphase mass transfer of solute from the solid phase to the liquid

phase, (kg/s).

n = number of solid particles (solids) used in the experiment.

N = Stirrer speed, (sec-1).

r = radius of the solid particles (solids) at any time, (m).

Re = ⎛ ⎝ ⎜ ⎞

⎠⎟dT ωπ

ν , Reynolds number (referred to the particle).

Sc = ρ Dv

, Schmidt number.

Sh =k

D LS

v

d , Sherwood number (referred to the particle).

t = time, (s).

T = vessel diameter, (m).

U = M

d ρ 3 , solid concentration.

VL = liquid volume, (m3).

μ = viscosity of liquid, (kg/m.s).

ρ = density of liquid, (kg/m3).



M5-6

ρs = solid density, (kg/m3).

ω = stirrer angular velocity, 2π N, (sec-1).

o = subscript indicating initial conditions.

ν = kinematic viscosity, (m2/s)



M5-7

Date:__________________

Log-sheet for Effect of Agitation on Solid Liquid Mass Transfer (Expt #M5).

Speed (rpm) 148 219

Type of impeller

Three bladed

45 Pitched

impeller

Six bladed

high

efficiency

impeller

Three bladed

45 Pitched

impeller

Six bladed

high

efficiency

impellerAverage diameter

of Solids (Take

diameter three

times for each

solid)

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

Time (min) Weight of the Solids Sample (gm)

0

3

6

9



M5-8

Figure 1: Schematic diagram of the agitator assembly

4 0 c m

8 c m

Vessel

Baffles

28.75 cm

Agitator

Speed

Regulator

Agitator Stand



H6-1

EXPERIMENT NO: H6

Heat Transfer in a Shell and Tube Heat

Exchanger

Objective

The objective of this experiment is to investigate heat transfer in a shell-and-

tube heat exchanger and to compute and compare the overall heat transfer

coefficient (U) for both co-current and counter-current modes of operation.

Introduction

Heat exchangers are widely used in the process industries so their design has

been highly developed. Most exchangers are liquid-to-liquid, but gas and non-

condensing vapors can also be treated in them.

The simple double-pipe exchanger is inadequate for flow rates that cannot

readily be handled in a few tubes. If several double pipes are used in parallel,

the weight of metal required for the outer tubes becomes large. The shell-and-

tube construction, such as that shown in Fig. 1, where one shell serves for

many tubes, is more economical. This exchanger, because it has one shell-side

pass and one tube-side pass, is a 1-1 exchanger.

In an exchanger the shell-side and tube-side heat-transfer coefficients are of

comparable importance, and both must be large if a satisfactory overall

coefficient is to be attained. The velocity and turbulence of the shell-side liquid

are as important as those of the tube-side liquid. To prevent weakening of thetube sheets there must be a minimum distance between the tubes. It is not

practicable to space the tubes so closely that the area of the path outside the

tubes is as small as that inside the tubes. If the two streams are of comparable

magnitude, the velocity on the shell side is low in comparison with that on the

tube side. Baffles are installed in the shell to decrease the cross section of the

shell-side liquid and to force the liquid to flow across the tube bank rather than

parallel with it. The added turbulence generated in this type of flow further

increases the shell-side coefficient.


The heat-transfer coefficient hi for the tube-side fluid in a shell-and-tubeexchanger can be calculated from the following equation:

( )[ ]( )

h

C G

Cp

k

D L

D G

i

p

i

i

μ

μ

⎛ ⎝ ⎜

⎞ ⎠⎟ =

+2 3 0 7

0 2

0 023 1 / .

.

. /

/ (1)



H6-2

The viscosity correction term is omitted in the above equation as well as in all

equations that follow since the temperature difference is not much. In this

equation the physical properties of the fluid, are evaluated at the bulk

temperature.

The coefficient for the shell-side ho cannot be so calculated because the

direction of flow is partly parallel to the tubes and partly across them and because the cross-sectional area of the stream and the mass velocity of the

stream vary as the fluid crosses the tube bundle back and forth across the shell.

Also, leakage between baffles and shell and between baffles and tubes short-

circuits some of the shell-side liquid and reduces the effectiveness of the

exchanger. An approximate but generally useful equation for predicting shell-

side coefficients is the Donohue equation (5), which is based on a weighted

average mass velocity Ge of the fluid flowing parallel with the tubes and that

flowing across the tubes. The mass velocity G b parallel with the tubes is the

mass flow rate divided by the free area for flow in the baffle window S b. (The

baffle window is the portion of the shell cross section not occupied by the

baffle). This area is the total area of the baffle window less the area occupied

by the tubes, or

S f D

N D

b bs

bo= −

π π2 2

4 4 (2)

where f b = fraction of the cross-sectional area of shell occupied by baffle

window

Ds = inside diameter of shell

N b = number of tubes in baffle window

Do = outside diameter of tubes

In crossflow the mass velocity passes through a local maximum each time the

fluid passes a row of tubes. For correlating purposes the mass velocity Gc for

cross-flow is based on the area Sc for transverse flow between the tubes in the

row at or closest to the centerline of the exchanger. In a large exchanger Sc can

be estimated from the equation

S PD D

pc so= −

⎛

⎝ ⎜

⎠⎟1 (3)

where p = center-to-center distance between tubes (1.65 cm)

P = baffle spacing (15 cm)

The mass velocities are then



H6-3

Gm

S and G

m

S b

c

b

c

c

c

= =

. .

(4)

The Donohue equation is

h D

k

D G C

k o o o e p

= ⎛

⎝ ⎜ ⎞

⎠⎟

⎛

⎝ ⎜

⎞

⎠⎟02

0 6 0 33

.

. .

μμ

(5)

where G G Ge b c= . This equation tends to give conservatively low values

of ho, especially at low Reynolds numbers. More elaborate methods of

estimating shell-side coefficients are available for the specialist. In j - factor

form Eq. (5) becomes

h

C G

C

k j

D Go

p e

p

oo e

μμ

⎛

⎝ ⎜

⎞

⎠⎟ = =

⎛ ⎝ ⎜ ⎞

⎠⎟

−2 3 0 4

0 2

/ .

. (6)

Correction of LMTD for cross flow

If a fluid flows perpendicularly to a heated or cooled tube bank, the LMTD, as

given by the equation

( )Δ

Δ ΔΔ Δ

T T T

T T L M =

−2 1

2 1ln / (7)

applies only if the temperature of one of the fluids is constant. If the

temperatures of both fluids change, the temperature conditions do not

correspond to either countercurrent or parallel flow but to a type of flow called

cross flow.

When flow types other than countercurrent or parallel appear, it is customary

to define a correction factor FG, which is so determined that when it is

multiplied by the LMTD for countercurrent flow, the product is the true

average temperature drop. Figure 2 shows a correlation for FG for crossflow

derived on the assumption that neither stream mixes with itself during flow

through the exchanger. FG = 1 for 1-1 heat exchanger.

Each curved line in the figure corresponds to a constant value of the

dimensionless ratio Z, defined as

Z T T

T T =

−−

4 5

3 1

(8)

and the abscissas are values of the dimensionless ratio H η , defined as:



H6-4

14

13

T T

T T H

−

−=η (9)

The factor Z is the ratio of the fall in temperature of the hot fluid to the rise in

temperature of the cold fluid. The factor ηH is the heating effectiveness, or the

ratio of the actual temperature rise of the cold fluid to the maximum possibletemperature rise obtainable if the warm-end approach were zero (based on

countercurrent flow). From the numerical values of ηH and Z the factor FG is

read from Fig. 2, interpolating between lines of constant Z where necessary,

and multiplied by the LMTD for counterflow to give the true mean temperature

drop.

The true mean temperature drop will be used in the following equation to

obtain overall heat transfer coefficient, U.

q UA T LM = Δ (10)

( )U

A

A h

A D D

k L h R Ro

i i

o o i

gl o

o i

=

+ + + +

1

2

1ln{ / }

π

(11)

Note: R o ≅ R i = 3.0 * 10-4

m2 oC w

-1.

where q could be calculated from the following equation which is applicable to

both hot and cold fluids.

( )q m H H b a= − (12)

Ha, H b = enthalpies per unit mass of stream at entrance and exit, respectively.


The test unit consists of a graphite heat exchanger and a shell-and-tube heat

exchanger. A schematic sketch showing valves, pressure gauges, rotameters,

and the location of temperature sensors is given in Figure 1. The hot water,

produced by the graphite heat exchanger using steam, is on the tube side. The

cold water on the shell side can be directed co-current or counter-current to the

hot water. Opening hand valve HV-3 while closing HV-6 and HV-7 will

implement the counter -current mode of operation. Reversing each valve

position will implement the co-current mode.

The length of the test section is 1 m with 37 tubes each of outside diameter

1.15 cm and of 1 mm thickness. The shell side has 4 baffles, each occupies

50% of its cross-sectional area, distanced 15 cm from each other. The inside

diameter of the shell side is 15 cm.



H6-5

A set of 6 thermocouples is provided to record pertinent process temperatures.

A selector switch and digital read-out are provided. The temperature indicators

shown in Figure 1 will measure the following temperatures.

T1 cold water inlet temperature

T2 hot water outlet temperature for the graphite heat exchanger

T3 cold water outlet temperature for shell and tube heat exchanger.

T4 hot water inlet temperature for the shell and tube heat exchanger

T5 hot water outlet temperature, for the shell and tube heat exchanger

T6 Steam temperature

Cold water is supplied through a rotameter with a range of 0 - 1.2 CFM. Note

the wedge at the side of the rotameter must be used to read the flow rate. Flows

are controlled through manual control valves upstream of the rotameters (HV-1

for hot water feed to the shell-and-tube heat exchanger, and HV-2 for that of

the cold water).


i) Keep HV-5 open all the time.

ii) Open HV-1 slowly.

iii) Open HV-8 slowly.

iv) Adjust HV-1 and HV-8 such that T2 is approximately 50oC - 60oC;

note that T2 should not exceed 85oC.

v) Choose the mode of operation in the shell and tube heat exchanger by

opening and closing the appropriate valves (start first in counter-current

mode, by opening HV-3 while closing HV-6 and HV-7).

vi) For a fixed hot water flow rate measure the following for six different

cold water flow rates:

a) cold water flow rate to the shell-and-tube heat exchanger

b) hot water flow rate to shell and tube heat exchanger via the

graphite heat exchanger

Three) cold water inlet

temperature

d) cold water outlet temperature



H6-6

Five) hot water inlet

temperature

Six) hot water outlet temperature

vii) Repeat the experiment with co-current flow conditions instead of thatof the counter-current (i.e. by closing HV-3 while opening HV-6 and

HV-7), but keep the hot water flow rate unchanged.

Shut Down Procedure - Shell and Tube Heat Exchanger

i) Close HV-8

ii) Close HV-1 and HV-2

iii) Close HV-4

iv) Close HV-3 and open HV-6

v) Leave the unit in a safe and clean condition


A set of six measurements will be taken for each mode of operation. The cold

water flow rate will be varied in the range 6.1 - 23.1 Liter/min. The hot water

flow rate and temperature will stay approximately constant at about 12.6

Liter/min and 55oC, respectively. Since the cold water for both the graphite

and the shell-and-tube heat exchangers is obtained from the same water main,

the cold water to the graphite heat exchanger must be checked whenever the

cold water to the shell and tube heat exchanger flow rate is changed. A log

sheet suitable to record all experimental data is attached.

Data Analysis

The following items must be covered in the analysis:

1) Carry out an energy balance for the tube-side and the shell side.

2) Compute the experimental overall heat transfer coefficient for the heat

exchanger.

3) Plot on a log-log scale the computed experimental overall heat transfercoefficient vs the shell-side Reynolds’s number.

4) Calculate the theoretical heat transfer coefficient and compare with the

experimental one.



H6-7

References:

Welty, J.R., Wicks, C.E., and Wilson, R.E., “Fundamentals of Momentum,

Heat and Mass Transfer”, 3rd edition, Wiley and Sons (1984)

Chapman, A.J., “Heat Transfer”, 4th edition, Macmillan Publishing Company(1989)

Notation:

A Area, (m2)

C p Specific heat at constant pressure, (kJ/kg.K)

D Diameter, (m); De, equivalent diameter of noncircular channel; Di,

inside diameter of tube; Do

, outside diameter of tube; Ds, inside

diameter of exchanger shell.

FG Correction factor for average temperature difference in crossflow or

multipass exchangers, dimensionless

f b Fraction of cross-sectional area of shell occupied by baffle window

(0.2)

G Mass velocity, (kg/m2-s); G b, in baffle window; Gc, in crossflow; Ge,

effective value in exchanger, G Gb c

.

h Individual heat-transfer coefficient, (W/m2.K); hc, for outside of coil,hi, for inside of tube; h j, for inner wall of jacket; ho for outside of tube

j j factor dimensionless; jo, for shell-side heat transfer

k gl Thermal conductivity, (W/m.K); k m, of tube wall

k Thermal conductivity, (W/m.K); k m, of the fluid

m Mass of liquid, (kg)

m

.

Flow rate, (kg/s); mc

.

, of cooling fluid

N b Number of tubes in baffle window

P Baffle pitch or spacing, (m)

p Center-to-center distance between tubes, (m)



H6-8

Q Quantity of heat, (J); Qr , total amount transferred during time interval tr

q Rate of heat transfer, (W)

S Cross-sectional area, (m2) ; S b, area for flow in baffle window; Sc, area

for crossflow in exchanger shell

T Temperature, (oC); at warm-fluid inlet; Thb, at warm-fluid outlet; Tr ,

reduced temperature; Ts, temperature of

U Overall heat-transfer coefficient, (W/m2.K); Ut, based on inside area

Z Ratio of temperature ranges in crossflow or multipass exchanger,

dimensionless [Eq. (15-6).



H6-9

Date:___________

Log-Sheet for Shell and Tube H.C.(Expt #H6)

Hot water flowrate:_______________

Cocurrent

Run

No.

Cold

Flow

T1 T3 T4 T5

Lit/min oC oC oC oC

1

2

3

4

5

6

Counter-Current

Run

No.

Cold

Flow

T1 T

3 T

4 T

5

Lit/min oC oC oC oC

1

2

3

4

5

6



H6-10

PI

T

PI

FI

FI

T 6

T

Condensate

PI

T2

Graphite Heat

Exchanger

HV-8

PCV

PC

V

HV-4

PI

HV-1

T 1

HV-2

HV-6

HV-3

HV-7

T4

T 5

PI

PI

HV-5

T 3

Tube Drain

HV Hand Valve

PI Pressure Indicator

PCV Pressure Control Valve

T Thermocouple

FI Flow Indicator - Rotameter

Figure 1: Schematic Diagram of Shell & Tube

Experiment



F5-1

EXPERIMENT NO: F5

Losses in Piping Systems

ObjectiveOne of the most common problems in fluid mechanics is the estimation of

pressure loss. It is the objective of this experiment to enable pressure loss

measurements to be made on several small bore pipe circuit components such

as pipe bends valves and sudden changes in area of flow.

Description of Apparatus

The apparatus is shown diagrammatically in Figure 1. There are essentially

two separate hydraulic circuits one painted dark blue, and the other painted

light blue, but having common inlet and outlets. A hydraulic bench is used tocirculate and measure water. Each one of the two pipe circuits contain a

number of pipe system components. The components in each of the circuits are

as follows:

Dark blue circuit 1. Gate Valve

2. Standard Elbow Bend

3. 90o Mitre Bend

4. Straight Pipe

Light blue circuit 5. Globe Valve

6. Sudden Expansion7. Sudden Contraction

8. 150 mm 90o Radius Bend



In all cases (except the gate and globe valves) the pressure change across each

of the component is measured by a pair of pressurized piezometer tubes. In the

case of the valves, pressure measurement is made by U-tubes containing

mercury.


For an incompressible fluid flowing through a pipe (Fig. 2) the following

equations apply:

( )Q V A V A continuity= =1 1 2 2 (1)

Z P g V g Z P g V g h L1 1 12

2 2 222 2

1 2+ + = + + +

−

/ / / / ρ ρ (2)



F5-2

(Bernoulli’s equation)

Head Loss

The head loss in a pipe circuit falls into two categories:

a) that due to viscous resistance extending throughout the total length of

the circuit

b) that due to localized affects such as valves, sudden changes in area of

flow and bends.

The overall head loss is a combination of both these categories. Because of the

mutual interference that exists between neighboring components in a complex

circuit, the total head loss may differ from that estimated from the losses due to

the individual components considered in isolation.

Head loss in straight pipes

The head loss along a length L of straight pipe of constant diameter d is given

by the expression:

h f L V gd f h gd

LV L L

= ⇒ =22

22 / (3)

where f is a dimensionless constant (i.e. friction factor) which is a function of

the Reynold's number of the flow and the roughness of the internal surface of

the pipe.

Head loss Due to Sudden Changes in Area of Flow

i) Sudden Expansion - The head loss at a sudden expansion is given by

(Figure 3) and its expression is:

hL = (V1-V2)2 /2 g (4)

ii) Sudden contraction - The head loss at a sudden contraction is given by


hL = KV22/2g (5)

where K is a dimensionless coefficient which depends upon the area ratio as

shown in Table I.

Table 1: Loss Coefficient for Sudden Contractions



F5-3

A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.l0

K 0.50 0.46 0.41 0.36 0.30 0.18 0.06 0

Head loss Due to Bends

The headloss due to a bend is given by the expression:

hB = K BV2/2g (6)

where K B is a dimensionless coefficient which depends on the bend

radius/pipe radius ratio and the angle of the bend. It should also be noted that

the loss given by this expression is not the total loss caused by the bend but the

excess loss above that which would be caused by a straight pipe equal in lengthto the length of the pipe axis.

Head loss Due to Valves

The head loss due to a valve is given by the expression:

hL = KV2/2g (7)

where the value of K depends upon the type of valve and degrees of opening.

Table 2 gives typical valves of loss coefficients for gate and globe valves.

Table 2: Loss Coefficient

Valve type K

Globe valve, fully open 10.0

Gate valve, fully open 0.2

Gate valve, half open 5.6





F5-5

Comparing equations 14 & 17:

hL = 12.6 x (18)


1. Open fully the water control on the hydraulic bench.

2. With the globe valve closed, open the gate valve fully to obtain

maximum flow through the dark blue circuit. Record the readings on

the piezometer tubes and the U-tube. Measure the flowrate by timing

the level rise in the volumetric tank.

3. Repeat the above procedure for a total of ten different flow rates

obtained by closing the gate valve, equally spaced over the full flow

range.

4. With a simple mercury in glass thermometer record the water

temperature in the sump tank.

5. Close the gate valve, open the globe valve and repeat the experimental

procedure for the light blue circuit.

NOTE: BEFORE SWITCHING OFF THE PUMP, CLOSE BOTH THE

GLOBE VALVE AND THE GATE VALVE. THIS PREVENTS

AIR GAINING ACCESS TO THE SYSTEM AND SO SAVES

TIME IN SUBSEQUENT SETTING UP.

Report (Data Analysis)

In addition to tables showing all experimental results, the report must

include the followings:

i) Dark blue circuit experiment

a) Obtain the relationship between the straight pipe head loss and the

volume flow rate (hL & Qn) by plotting log h L against log Q (log hL vs.

log Q).

b) Plot friction factor data versus Reynold's number for the straight pipe

(L = 0.914 m, D = 13.7 mm). Also, obtain relationship between f &

Ren, by plotting log f against log Re. Comment on your result by

comparing with the literature given equations (i.e f =0.04 Re-0.16

for

4000<Re<107 & f = 0.079 Re

-1/4 for 4000< Re < 10

5 ).

c) Obtain the value of K for the gate valve when it is fully opened and

compare with literature (Table 2).



F5-6

d) Discuss head losses in 90° Mitre and Standard Elbow bend.

i) Light blue circuit experiment

a) If head rise across a sudden expansion(13.7 mm / 26.4 mm) is given by

expressiong

V h L

2

396.0 21= .Compare this head rise with the measured

head rise. Plot the measured and the calculated head rise.

b) If head loss due to sudden contraction (26.4 mm / 13.7 mm) is given by

the expressiong

V h L

2

303.1 2

2= . Compare this fall in the head with the

measured head loss. Plot the measured and calculated fall in head due

to sudden contraction.

c) Obtain the value of K for the globe valve when it is fully opened andcompare with literature (Table 2).

d) What is the effect of bend radius on head losses?

Reference:

Beek, W.J. & K.M. Muttzall, Transport Phenomena, John Wiley (1975).

Denn, M.M. Process Fluid Mechanics, Prentice-Hall (1980).

de Nevers, Noel, Fluid Mechanics for Chemical Engineers, McGraw-Hill,

Singapore (1991)

Notation:

Q volumetric flowrate, (m3/s)

V mean velocity, (m/s)

A cross-sectional area, (m2)

Z height above datum, (m)

P static pressure, (N/m2)

hL head loss, (m)

ρ density, (kg/m3)

g acceleration due to gravity, (9.81 m/s2)



F5-7

f Friction factor

d Diameter of pipe, (m)

L Length of pipe, (m)

K Loss Coefficient

K B Loss coefficient due to bends

Re Reynolds Number

Prepared by: Mr. N. M. Tukur



F5-8

Identification of Manometer Tubes & Components

Manometer Unit

1 Standard elbow bend

2

3 Straight Pipe

4

5 90o Mitre Bend

6

7 Expansion

8

9 Contraction

10

11 100 mm bend

12

13 150 mm bend

14

15 50 mm bend16



F5-9

Date:_______________

EXPERIMENTAL RESULTS FOR DARK BLUE CIRCUIT(Expt#F5)

Test # Flowrate

Piezometer tube Readings

(mm) water

U-Tube

(mm) Hg

Vol.

(Liter)

Time

(s)

1 2 3 4 5 6 Gate

Valve

*1

2

3

4

5

6

7

8

9

10

*Valve fully open Water Temperature =



F5-10

Date:_____________

EXPERIMENTAL RESULTS FOR LIGHT BLUE CIRCUIT(Expt#F5)

Test # Flowrate Piezometer tube Readings

(mm) water

U-Tube

(mm) Hg

Vol.

(Liter)

Time

(s)

7 8 9 10 11 12 13 14 15 16 Globe

Valve

*11

12

13

14

15

16

17

18

19

20




F5-11

C

H

J

D

K

EL F

A

From Bench Tank

To Weigh Tank

Ma

P.V.C. Manometer Tubes

Fig. 1: Diagrammatic Arrangement of Apparatus AAppar

A Straight Pipe 13.7 mm Bore

B 90o Sharp Bend

C Proprietary 90o Elbow

D Gate Valve

E Sudden Enlargement - 13.7 mm / 26.4 mm

F Sudden Contraction - 26.4 mm / 13.7 mm

G Smooth 90o Bend 52 mm Radius

H Smooth 90o Bend 102 mm Radius

J Smooth 90o Bend 152 mm Radius

K Globe Valve

L Straight Pipe 26.4 mm Bore.



F5-12

.

.1

2

ρ

Datum

V1

ρ 1

A1

V2

ρ 2

A2

Z1

Z2

Q

Fig. 2: An Incompressible Fluid Flowing Through a Pipe.



F5-13

A1

V1

A2

V2

Fig. 3: A Sudden Expansion.

A1

V1

A2

V2

Fig. 4: A Sudden Contraction.



F5-14

Fig. 5: Pressurized Piezzometer Tubes to measure Pressure Loss between

two points at different elevations.

P1

P2

2

1Air at

Pressure

x

y

z

Fig. 6: U-Tube containing mercury used to

measure Pressure Loss across valves.

O O

x

y

Mercury

Water

2 1

P2 P1



M5-1

EXPERIMENT No: M5

Effect of Agitation on Solid Liquid Mass Transfer

Objective

The objective of this experiment is to study the dissolution of solid spherical particles

in an agitated liquid using different types of agitators and to determine experimentally

the interphase mass transfer coefficient.


A schematic diagram of the equipment is illustrated in Figure 1. The apparatus

basically consists of an agitated vessel of 28.75 cm in diameter and 40 cm in height,

sour ball solids of diameter in the range of 1.5 to 2.5 cm, distilled water as a

dissolving liquid, two type of impellers, a ladle, weighing balance, and a drain valve.

The agitated vessel is provided with a lid on the top of the tank with a slot up to the

center, which allows the shaft of impeller to pass through the lid. The lid prevents any

splashing of liquid during agitation. Four standard baffles are provided in the vessel,

which inhibit the formation of vortex during agitation.

The types of impeller are: a three-bladed 45° pitched-blade impeller and a six-bladed

high-efficiency impeller. The diameter of both impellers is 10 cm. The impeller

bottom clearance is kept one-fourth of tank diameter. The sourball solid is composed

of a mixture of sugar, citric acid, and color additives. This material is inexpensive and

safe, and its high solubility allows a number of successive experimental runs to be

made with a single liquid batch. Since the particle size and shape changes during the

experiment, the mass transfer might also change. Therefore, for the sake of simplicityit is assumed that the shape of particles and interphase mass transfer coefficient do not

change and are representative of the entire experiment.


Solid-liquid mass transfer is important in many industrial processes such as

dissolution, crystallization, solid-liquid extraction, fermentation, etc. Agitated vessels

are often used because they are effective in suspending solids particles, ensuring that

all the surface area available is utilized and because they lead to good transfer rates

[1].

The rate of mass transfer between a solid and an agitated liquid is usually described

by the following relation (1-3).

( ) LSAT LS

C C Ak m −=& (1)

The experiment is conducted on a batch system, with the result that a transient mass

balance on the dissolving solid takes the form



M5-2

( ) LSAT LS

C C Ak mdt

dM −−=−= & (2)

while the corresponding mass balance on the liquid phase is

( ) LSAT LS

L

L C C Ak m

dt

dC V −== & (3)

These model equations are coupled through the liquid concentration term and must be

solved simultaneously. The solution procedure can be simplified by noting that the

total amount of solid distributed in the solid and liquid phases remain constant at any

instant.

M V C M V C o L Lo L L+ = + (4)

This equation can be combined with Eq. (2) and solved to yield the model predictions.

However, as the solids dissolve, they change their size and shape, and the resulting

changes in the interfacial area should be taken into account before the model

equations can be solved. In this analysis, any effect of changing particle size on the

interphase mass transfer coefficient is ignored.

The sourball solids studied in the experiment are initially spherical and are assumed

to retain their spherical shape as they dissolve. The solids are also of same initial size,

and it is assumed that all of the solids dissolve at the same rate. Under these

assumptions, the mass of the solids remaining in the solid phase at any time for a

system of n balls with radius ‘r’, is

M r ns= 4

33

π ρ (5)

the corresponding interfacial area is

A r n= 4 2

π (6)

and the value of C SAT

is experimentally found to be 1613 kg/m3 at 20 °C.

Substitution of Eqs. (4), (5), and (6) into Eq. (2) yields the form of the model equationthat can be solved for the mass of candies remaining in the solid phase at any time,

dM

dt k

nM C C

M M

V LS

s

SAT LO

o

L

= − ⎡

⎣⎢⎤

⎦⎥ − +

−⎛ ⎝ ⎜ ⎞

⎠⎟

⎡

⎣⎢⎤

⎦⎥36

2

2

1 3

π

ρ

/

(7)



M5-3

This equation can be solved numerically, but an analytical solution is possible if the

liquid phase concentration ( )C L is always much less than saturated concentration

( )C C L SAT << and can be neglected. Under these conditions, Eq. (7) can be

integrated to yield the following relation between time and the fraction of remaining

solid phase.

M

M

n

M k C t

o o s

LS SAT = −⎛

⎝ ⎜

⎞

⎠⎟

⎡

⎣⎢

⎤

⎦⎥1

4

3 2

1 3 3

π

ρ

/

(8)

Boon-Long (1) developed a correlation for mass transfer from suspended solids to a

liquid in agitated vessels as follows:

Sh = 0.046 Re0.283

Ga0.173

U-0.011

(T/d)0.019

Sc0.461

(9)

The above correlation is quite useful in comparing with experimental results.


1. Close the drain valve of the agitated vessel.

2. Fill the agitated vessel with distilled water up to the mark equivalent to the

diameter of the vessel, and measure its volume.

3. Hook-up either type of impeller to the agitator assembly with the help of an

allen-key.

4. Take three sourball solids, weigh and measure their average diameter.

5. Start the agitator. Adjust the speed of impeller to 148 rpm (2 on scale) with the

help of a small wheel located on the top right hand side of the agitator, then

stop the agitator.

6. Put the solids into the vessel and start the agitator.

7. After 3 minutes of dissolution, stop the agitator and remove the balls with the

help of a ladle, dry them with a tissue paper, weigh them, and put them back

into the vessel.

8. Repeat the steps 6 and 7 for 3 to 4 times.

9. Add fresh three solids into the vessel having measured their weights and

average diameter.

10. Start the agitator and adjust the speed to 219 rpm (4 on the scale), and then

repeat steps 6 to 8.



M5-4

11. Remove the impeller and replace it with the other type of impeller.

12. Repeat steps 4 to 10 in order to obtain a new set of data for the second type of

impeller.

IMPORTANT: Do not adjust the speed of impeller while the motor of agitator isstopped.


In accordance with the procedures given earlier the following will be measured and

observed:

(i) Measure the volume of the distilled water charged to the vessel, and the average

diameter & weight of solids.

(ii) Measure the loss of wt. of solids with time.

(iii) Measure the loss of wt. of solids with change in the rpm of impeller.

(iv) Measure the loss of wt. of solids by using the different types of impellers.

Data Analysis

(i) Plot a graph of (M/Mo)1/3

vs t for each of the two different types of impeller and

the two speeds using equation (8). Obtain k Ls

from these graphs.

(ii) Plot a graph of mass transfer coefficient ( )k LS vs. agitation speed (rpm) for the

two types of impeller.

(iii) Compare the k Ls (exp) with k Ls (theoretical).

REFERENCES.

1. S. Boon-Long, C. Laguerie and J.P. Coudere "Mass Transfer from suspended solids

to a liquid in Agitated Vessels", Chem. Eng. Sci., 33, p. 813 (1978).

2. Nienow, A.W., "The Mixer as a Reactor: Liquid/Solid Systems", Chapter 18 ofMixing in the Process Industries, edited by N. Harnby, M.F. Edwards, and A.W.

Nienow, Butterworths, London (1985).

3. M. Elizabeth Sensel and Kevin J. Myers, "Add some Flavor to your Agitation

Experiment", Chem. Eng. Ed., 26 (3), p. 156 (1992).

NOTATION:



M5-5

A = total liquid-solid interfacial area at any time, (m2).

C L = liquid-phase concentration of the solute, (kg/m3).

C SAT =equilibrium liquid-phase concentration of the solute, (kg/m3).

d = Particle diameter, (m).

Dν= Diffusivity of solid ball (sucrose) into water, (m2/s).

g = gravitational constant, (m/sec2).

Ga gd

= ρ

μ

2 3

2. , Gallileo number

k LS =liquid-solid interphase mass transfer coefficient, (m/s).

M = total mass of the solute (solids) remaining in the solid-phase at any time, (kg).

m& = rate of interphase mass transfer of solute from the solid phase to the liquid

phase, (kg/s).

n = number of solid particles (solids) used in the experiment.

N = Stirrer speed, (sec-1).

r = radius of the solid particles (solids) at any time, (m).

Re = ⎛ ⎝ ⎜ ⎞

⎠⎟dT ωπ

ν , Reynolds number (referred to the particle).

Sc = ρ Dv

, Schmidt number.

Sh =k

D LS

v

d , Sherwood number (referred to the particle).

t = time, (s).

T = vessel diameter, (m).

U = M

d ρ 3 , solid concentration.

VL = liquid volume, (m3).

μ = viscosity of liquid, (kg/m.s).

ρ = density of liquid, (kg/m3).



M5-6

ρs = solid density, (kg/m3).

ω = stirrer angular velocity, 2π N, (sec-1).

o = subscript indicating initial conditions.

ν = kinematic viscosity, (m2/s)



M5-7

Date:__________________

Log-sheet for Effect of Agitation on Solid Liquid Mass Transfer (Expt #M5).

Speed (rpm) 148 219

Type of impeller

Three bladed

45 Pitched

impeller

Six bladed

high

efficiency

impeller

Three bladed

45 Pitched

impeller

Six bladed

high

efficiency

impellerAverage diameter

of Solids (Take

diameter three

times for each

solid)

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

d 11 d 12 d 13

d avg =

Time (min) Weight of the Solids Sample (gm)

0

3

6

9



M5-8

Figure 1: Schematic diagram of the agitator assembly

4 0 c m

8 c m

Vessel

Baffles

28.75 cm

Agitator

Speed

Regulator

Agitator Stand



H6-1

EXPERIMENT NO: H6

Heat Transfer in a Shell and Tube Heat

Exchanger

Objective

The objective of this experiment is to investigate heat transfer in a shell-and-

tube heat exchanger and to compute and compare the overall heat transfer

coefficient (U) for both co-current and counter-current modes of operation.

Introduction

Heat exchangers are widely used in the process industries so their design has

been highly developed. Most exchangers are liquid-to-liquid, but gas and non-

condensing vapors can also be treated in them.

The simple double-pipe exchanger is inadequate for flow rates that cannot

readily be handled in a few tubes. If several double pipes are used in parallel,

the weight of metal required for the outer tubes becomes large. The shell-and-

tube construction, such as that shown in Fig. 1, where one shell serves for

many tubes, is more economical. This exchanger, because it has one shell-side

pass and one tube-side pass, is a 1-1 exchanger.

In an exchanger the shell-side and tube-side heat-transfer coefficients are of

comparable importance, and both must be large if a satisfactory overall

coefficient is to be attained. The velocity and turbulence of the shell-side liquid

are as important as those of the tube-side liquid. To prevent weakening of thetube sheets there must be a minimum distance between the tubes. It is not

practicable to space the tubes so closely that the area of the path outside the

tubes is as small as that inside the tubes. If the two streams are of comparable

magnitude, the velocity on the shell side is low in comparison with that on the

tube side. Baffles are installed in the shell to decrease the cross section of the

shell-side liquid and to force the liquid to flow across the tube bank rather than

parallel with it. The added turbulence generated in this type of flow further

increases the shell-side coefficient.


The heat-transfer coefficient hi for the tube-side fluid in a shell-and-tubeexchanger can be calculated from the following equation:

( )[ ]( )

h

C G

Cp

k

D L

D G

i

p

i

i

μ

μ

⎛ ⎝ ⎜

⎞ ⎠⎟ =

+2 3 0 7

0 2

0 023 1 / .

.

. /

/ (1)



H6-2

The viscosity correction term is omitted in the above equation as well as in all

equations that follow since the temperature difference is not much. In this

equation the physical properties of the fluid, are evaluated at the bulk

temperature.

The coefficient for the shell-side ho cannot be so calculated because the

direction of flow is partly parallel to the tubes and partly across them and because the cross-sectional area of the stream and the mass velocity of the

stream vary as the fluid crosses the tube bundle back and forth across the shell.

Also, leakage between baffles and shell and between baffles and tubes short-

circuits some of the shell-side liquid and reduces the effectiveness of the

exchanger. An approximate but generally useful equation for predicting shell-

side coefficients is the Donohue equation (5), which is based on a weighted

average mass velocity Ge of the fluid flowing parallel with the tubes and that

flowing across the tubes. The mass velocity G b parallel with the tubes is the

mass flow rate divided by the free area for flow in the baffle window S b. (The

baffle window is the portion of the shell cross section not occupied by the

baffle). This area is the total area of the baffle window less the area occupied

by the tubes, or

S f D

N D

b bs

bo= −

π π2 2

4 4 (2)

where f b = fraction of the cross-sectional area of shell occupied by baffle

window

Ds = inside diameter of shell

N b = number of tubes in baffle window

Do = outside diameter of tubes

In crossflow the mass velocity passes through a local maximum each time the

fluid passes a row of tubes. For correlating purposes the mass velocity Gc for

cross-flow is based on the area Sc for transverse flow between the tubes in the

row at or closest to the centerline of the exchanger. In a large exchanger Sc can

be estimated from the equation

S PD D

pc so= −

⎛

⎝ ⎜

⎠⎟1 (3)

where p = center-to-center distance between tubes (1.65 cm)

P = baffle spacing (15 cm)

The mass velocities are then



H6-3

Gm

S and G

m

S b

c

b

c

c

c

= =

. .

(4)

The Donohue equation is

h D

k

D G C

k o o o e p

= ⎛

⎝ ⎜ ⎞

⎠⎟

⎛

⎝ ⎜

⎞

⎠⎟02

0 6 0 33

.

. .

μμ

(5)

where G G Ge b c= . This equation tends to give conservatively low values

of ho, especially at low Reynolds numbers. More elaborate methods of

estimating shell-side coefficients are available for the specialist. In j - factor

form Eq. (5) becomes

h

C G

C

k j

D Go

p e

p

oo e

μμ

⎛

⎝ ⎜

⎞

⎠⎟ = =

⎛ ⎝ ⎜ ⎞

⎠⎟

−2 3 0 4

0 2

/ .

. (6)

Correction of LMTD for cross flow

If a fluid flows perpendicularly to a heated or cooled tube bank, the LMTD, as

given by the equation

( )Δ

Δ ΔΔ Δ

T T T

T T L M =

−2 1

2 1ln / (7)

applies only if the temperature of one of the fluids is constant. If the

temperatures of both fluids change, the temperature conditions do not

correspond to either countercurrent or parallel flow but to a type of flow called

cross flow.

When flow types other than countercurrent or parallel appear, it is customary

to define a correction factor FG, which is so determined that when it is

multiplied by the LMTD for countercurrent flow, the product is the true

average temperature drop. Figure 2 shows a correlation for FG for crossflow

derived on the assumption that neither stream mixes with itself during flow

through the exchanger. FG = 1 for 1-1 heat exchanger.

Each curved line in the figure corresponds to a constant value of the

dimensionless ratio Z, defined as

Z T T

T T =

−−

4 5

3 1

(8)

and the abscissas are values of the dimensionless ratio H η , defined as:



H6-4

14

13

T T

T T H

−

−=η (9)

The factor Z is the ratio of the fall in temperature of the hot fluid to the rise in

temperature of the cold fluid. The factor ηH is the heating effectiveness, or the

ratio of the actual temperature rise of the cold fluid to the maximum possibletemperature rise obtainable if the warm-end approach were zero (based on

countercurrent flow). From the numerical values of ηH and Z the factor FG is

read from Fig. 2, interpolating between lines of constant Z where necessary,

and multiplied by the LMTD for counterflow to give the true mean temperature

drop.

The true mean temperature drop will be used in the following equation to

obtain overall heat transfer coefficient, U.

q UA T LM = Δ (10)

( )U

A

A h

A D D

k L h R Ro

i i

o o i

gl o

o i

=

+ + + +

1

2

1ln{ / }

π

(11)

Note: R o ≅ R i = 3.0 * 10-4

m2 oC w

-1.

where q could be calculated from the following equation which is applicable to

both hot and cold fluids.

( )q m H H b a= − (12)

Ha, H b = enthalpies per unit mass of stream at entrance and exit, respectively.


The test unit consists of a graphite heat exchanger and a shell-and-tube heat

exchanger. A schematic sketch showing valves, pressure gauges, rotameters,

and the location of temperature sensors is given in Figure 1. The hot water,

produced by the graphite heat exchanger using steam, is on the tube side. The

cold water on the shell side can be directed co-current or counter-current to the

hot water. Opening hand valve HV-3 while closing HV-6 and HV-7 will

implement the counter -current mode of operation. Reversing each valve

position will implement the co-current mode.

The length of the test section is 1 m with 37 tubes each of outside diameter

1.15 cm and of 1 mm thickness. The shell side has 4 baffles, each occupies

50% of its cross-sectional area, distanced 15 cm from each other. The inside

diameter of the shell side is 15 cm.



H6-5

A set of 6 thermocouples is provided to record pertinent process temperatures.

A selector switch and digital read-out are provided. The temperature indicators

shown in Figure 1 will measure the following temperatures.

T1 cold water inlet temperature

T2 hot water outlet temperature for the graphite heat exchanger

T3 cold water outlet temperature for shell and tube heat exchanger.

T4 hot water inlet temperature for the shell and tube heat exchanger

T5 hot water outlet temperature, for the shell and tube heat exchanger

T6 Steam temperature

Cold water is supplied through a rotameter with a range of 0 - 1.2 CFM. Note

the wedge at the side of the rotameter must be used to read the flow rate. Flows

are controlled through manual control valves upstream of the rotameters (HV-1

for hot water feed to the shell-and-tube heat exchanger, and HV-2 for that of

the cold water).


i) Keep HV-5 open all the time.

ii) Open HV-1 slowly.

iii) Open HV-8 slowly.

iv) Adjust HV-1 and HV-8 such that T2 is approximately 50oC - 60oC;

note that T2 should not exceed 85oC.

v) Choose the mode of operation in the shell and tube heat exchanger by

opening and closing the appropriate valves (start first in counter-current

mode, by opening HV-3 while closing HV-6 and HV-7).

vi) For a fixed hot water flow rate measure the following for six different

cold water flow rates:

a) cold water flow rate to the shell-and-tube heat exchanger

b) hot water flow rate to shell and tube heat exchanger via the

graphite heat exchanger

Three) cold water inlet

temperature

d) cold water outlet temperature



H6-6

Five) hot water inlet

temperature

Six) hot water outlet temperature

vii) Repeat the experiment with co-current flow conditions instead of thatof the counter-current (i.e. by closing HV-3 while opening HV-6 and

HV-7), but keep the hot water flow rate unchanged.

Shut Down Procedure - Shell and Tube Heat Exchanger

i) Close HV-8

ii) Close HV-1 and HV-2

iii) Close HV-4

iv) Close HV-3 and open HV-6

v) Leave the unit in a safe and clean condition


A set of six measurements will be taken for each mode of operation. The cold

water flow rate will be varied in the range 6.1 - 23.1 Liter/min. The hot water

flow rate and temperature will stay approximately constant at about 12.6

Liter/min and 55oC, respectively. Since the cold water for both the graphite

and the shell-and-tube heat exchangers is obtained from the same water main,

the cold water to the graphite heat exchanger must be checked whenever the

cold water to the shell and tube heat exchanger flow rate is changed. A log

sheet suitable to record all experimental data is attached.

Data Analysis

The following items must be covered in the analysis:

1) Carry out an energy balance for the tube-side and the shell side.

2) Compute the experimental overall heat transfer coefficient for the heat

exchanger.

3) Plot on a log-log scale the computed experimental overall heat transfercoefficient vs the shell-side Reynolds’s number.

4) Calculate the theoretical heat transfer coefficient and compare with the

experimental one.



H6-7

References:

Welty, J.R., Wicks, C.E., and Wilson, R.E., “Fundamentals of Momentum,

Heat and Mass Transfer”, 3rd edition, Wiley and Sons (1984)

Chapman, A.J., “Heat Transfer”, 4th edition, Macmillan Publishing Company(1989)

Notation:

A Area, (m2)

C p Specific heat at constant pressure, (kJ/kg.K)

D Diameter, (m); De, equivalent diameter of noncircular channel; Di,

inside diameter of tube; Do

, outside diameter of tube; Ds, inside

diameter of exchanger shell.

FG Correction factor for average temperature difference in crossflow or

multipass exchangers, dimensionless

f b Fraction of cross-sectional area of shell occupied by baffle window

(0.2)

G Mass velocity, (kg/m2-s); G b, in baffle window; Gc, in crossflow; Ge,

effective value in exchanger, G Gb c

.

h Individual heat-transfer coefficient, (W/m2.K); hc, for outside of coil,hi, for inside of tube; h j, for inner wall of jacket; ho for outside of tube

j j factor dimensionless; jo, for shell-side heat transfer

k gl Thermal conductivity, (W/m.K); k m, of tube wall

k Thermal conductivity, (W/m.K); k m, of the fluid

m Mass of liquid, (kg)

m

.

Flow rate, (kg/s); mc

.

, of cooling fluid

N b Number of tubes in baffle window

P Baffle pitch or spacing, (m)

p Center-to-center distance between tubes, (m)



H6-8

Q Quantity of heat, (J); Qr , total amount transferred during time interval tr

q Rate of heat transfer, (W)

S Cross-sectional area, (m2) ; S b, area for flow in baffle window; Sc, area

for crossflow in exchanger shell

T Temperature, (oC); at warm-fluid inlet; Thb, at warm-fluid outlet; Tr ,

reduced temperature; Ts, temperature of

U Overall heat-transfer coefficient, (W/m2.K); Ut, based on inside area

Z Ratio of temperature ranges in crossflow or multipass exchanger,

dimensionless [Eq. (15-6).



H6-9

Date:___________

Log-Sheet for Shell and Tube H.C.(Expt #H6)

Hot water flowrate:_______________

Cocurrent

Run

No.

Cold

Flow

T1 T3 T4 T5

Lit/min oC oC oC oC

1

2

3

4

5

6

Counter-Current

Run

No.

Cold

Flow

T1 T

3 T

4 T

5

Lit/min oC oC oC oC

1

2

3

4

5

6



H6-10

PI

T

PI

FI

FI

T 6

T

Condensate

PI

T2

Graphite Heat

Exchanger

HV-8

PCV

PC

V

HV-4

PI

HV-1

T 1

HV-2

HV-6

HV-3

HV-7

T4

T 5

PI

PI

HV-5

T 3

Tube Drain

HV Hand Valve

PI Pressure Indicator

PCV Pressure Control Valve

T Thermocouple

FI Flow Indicator - Rotameter

Figure 1: Schematic Diagram of Shell & Tube

Experiment



F5-1

EXPERIMENT NO: F5

Losses in Piping Systems

ObjectiveOne of the most common problems in fluid mechanics is the estimation of

pressure loss. It is the objective of this experiment to enable pressure loss

measurements to be made on several small bore pipe circuit components such

as pipe bends valves and sudden changes in area of flow.

Description of Apparatus

The apparatus is shown diagrammatically in Figure 1. There are essentially

two separate hydraulic circuits one painted dark blue, and the other painted

light blue, but having common inlet and outlets. A hydraulic bench is used tocirculate and measure water. Each one of the two pipe circuits contain a

number of pipe system components. The components in each of the circuits are

as follows:

Dark blue circuit 1. Gate Valve

2. Standard Elbow Bend

3. 90o Mitre Bend

4. Straight Pipe

Light blue circuit 5. Globe Valve

6. Sudden Expansion7. Sudden Contraction




In all cases (except the gate and globe valves) the pressure change across each

of the component is measured by a pair of pressurized piezometer tubes. In the

case of the valves, pressure measurement is made by U-tubes containing

mercury.


For an incompressible fluid flowing through a pipe (Fig. 2) the following

equations apply:

( )Q V A V A continuity= =1 1 2 2 (1)

Z P g V g Z P g V g h L1 1 12

2 2 222 2

1 2+ + = + + +

−

/ / / / ρ ρ (2)



F5-2

(Bernoulli’s equation)

Head Loss

The head loss in a pipe circuit falls into two categories:

a) that due to viscous resistance extending throughout the total length of

the circuit

b) that due to localized affects such as valves, sudden changes in area of

flow and bends.

The overall head loss is a combination of both these categories. Because of the

mutual interference that exists between neighboring components in a complex

circuit, the total head loss may differ from that estimated from the losses due to

the individual components considered in isolation.

Head loss in straight pipes

The head loss along a length L of straight pipe of constant diameter d is given

by the expression:

h f L V gd f h gd

LV L L

= ⇒ =22

22 / (3)

where f is a dimensionless constant (i.e. friction factor) which is a function of

the Reynold's number of the flow and the roughness of the internal surface of

the pipe.

Head loss Due to Sudden Changes in Area of Flow

i) Sudden Expansion - The head loss at a sudden expansion is given by


hL = (V1-V2)2 /2 g (4)

ii) Sudden contraction - The head loss at a sudden contraction is given by


hL = KV22/2g (5)

where K is a dimensionless coefficient which depends upon the area ratio as

shown in Table I.

Table 1: Loss Coefficient for Sudden Contractions



F5-3

A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.l0

K 0.50 0.46 0.41 0.36 0.30 0.18 0.06 0

Head loss Due to Bends

The headloss due to a bend is given by the expression:

hB = K BV2/2g (6)

where K B is a dimensionless coefficient which depends on the bend

radius/pipe radius ratio and the angle of the bend. It should also be noted that

the loss given by this expression is not the total loss caused by the bend but the

excess loss above that which would be caused by a straight pipe equal in lengthto the length of the pipe axis.

Head loss Due to Valves

The head loss due to a valve is given by the expression:

hL = KV2/2g (7)

where the value of K depends upon the type of valve and degrees of opening.

Table 2 gives typical valves of loss coefficients for gate and globe valves.

Table 2: Loss Coefficient

Valve type K

Globe valve, fully open 10.0

Gate valve, fully open 0.2

Gate valve, half open 5.6



F5-4

Principles of Pressure Loss Measurements

a) Pressure Loss Between Two Points at Different Elevations

Considering Fig. 5, applying Bernoulli's equation between 1 & 2, gives:

Z + P1/ρg + V12/2g = P2/ ρg + V2

2/2g + hL (8)

but V1 = V2, ⇒ hL = Z + P1 - P2/ρg (9)

Consider piezometer tubes:

P = P1 + ρg[Z - (x + y)] (10)

also P = P2 - ρgy (11)

giving: x = Z + (P1 - P2) / (ρg) (12)

Comparing equations 9 and 12 gives:

hL = x (13)

b) Pressure Loss Across Valves

Considering Fig. 6, since 1 & 2 have the same elevation and pipe diameter;

Bernoulli's equation when applied between 1 & 2 becomes:

P1/ρg = P2/ρg + hL (14)

hL = (P1 - P2) / (ρH2 O g)

Consider U-tube. Pressure in both limbs of U-tube are equal at level 00.

Therefore equating pressures at 00:

P2 -ρH2O (x + y) + ρHg

gx = P1 - ρH2O gy (15)

giving, P1 - P2 = xg (ρHg - ρH2O) (16)

hence, P1 - P2 = xg ρH2O (ρHg/ρH2O - 1)

P1 - P2 / g ρ H2O x (ρHg/ρH2O -1)

Taking ρHg / ρH2O = S (specific gravity of mercury, 13.6)

P1 - P2 / g ρH2O = x(S - 1) = 12.6x (17)



F5-5

Comparing equations 14 & 17:

hL = 12.6 x (18)


1. Open fully the water control on the hydraulic bench.

2. With the globe valve closed, open the gate valve fully to obtain

maximum flow through the dark blue circuit. Record the readings on

the piezometer tubes and the U-tube. Measure the flowrate by timing

the level rise in the volumetric tank.

3. Repeat the above procedure for a total of ten different flow rates

obtained by closing the gate valve, equally spaced over the full flow

range.

4. With a simple mercury in glass thermometer record the water

temperature in the sump tank.

5. Close the gate valve, open the globe valve and repeat the experimental

procedure for the light blue circuit.

NOTE: BEFORE SWITCHING OFF THE PUMP, CLOSE BOTH THE

GLOBE VALVE AND THE GATE VALVE. THIS PREVENTS

AIR GAINING ACCESS TO THE SYSTEM AND SO SAVES

TIME IN SUBSEQUENT SETTING UP.

Report (Data Analysis)

In addition to tables showing all experimental results, the report must

include the followings:

i) Dark blue circuit experiment

a) Obtain the relationship between the straight pipe head loss and the

volume flow rate (hL & Qn) by plotting log h L against log Q (log hL vs.

log Q).

b) Plot friction factor data versus Reynold's number for the straight pipe

(L = 0.914 m, D = 13.7 mm). Also, obtain relationship between f &

Ren, by plotting log f against log Re. Comment on your result by

comparing with the literature given equations (i.e f =0.04 Re-0.16

for

4000<Re<107 & f = 0.079 Re

-1/4 for 4000< Re < 10

5 ).

c) Obtain the value of K for the gate valve when it is fully opened and

compare with literature (Table 2).





F5-7

f Friction factor

d Diameter of pipe, (m)

L Length of pipe, (m)

K Loss Coefficient

K B Loss coefficient due to bends

Re Reynolds Number

Prepared by: Mr. N. M. Tukur



F5-8

Identification of Manometer Tubes & Components

Manometer Unit

1 Standard elbow bend

2

3 Straight Pipe

4

5 90o Mitre Bend

6

7 Expansion

8

9 Contraction

10

11 100 mm bend

12

13 150 mm bend

14

15 50 mm bend16



F5-9

Date:_______________

EXPERIMENTAL RESULTS FOR DARK BLUE CIRCUIT(Expt#F5)

Test # Flowrate

Piezometer tube Readings

(mm) water

U-Tube

(mm) Hg

Vol.

(Liter)

Time

(s)

1 2 3 4 5 6 Gate

Valve

*1

2

3

4

5

6

7

8

9

10




F5-10

Date:_____________

EXPERIMENTAL RESULTS FOR LIGHT BLUE CIRCUIT(Expt#F5)

Test # Flowrate Piezometer tube Readings

(mm) water

U-Tube

(mm) Hg

Vol.

(Liter)

Time

(s)

7 8 9 10 11 12 13 14 15 16 Globe

Valve

*11

12

13

14

15

16

17

18

19

20




F5-11

C

H

J

D

K

EL F

A

From Bench Tank

To Weigh Tank

Ma

P.V.C. Manometer Tubes

Fig. 1: Diagrammatic Arrangement of Apparatus AAppar

A Straight Pipe 13.7 mm Bore

B 90o Sharp Bend

C Proprietary 90o Elbow

D Gate Valve

E Sudden Enlargement - 13.7 mm / 26.4 mm

F Sudden Contraction - 26.4 mm / 13.7 mm

G Smooth 90o Bend 52 mm Radius

H Smooth 90o Bend 102 mm Radius

J Smooth 90o Bend 152 mm Radius

K Globe Valve

L Straight Pipe 26.4 mm Bore.



F5-12

.

.1

2

ρ

Datum

V1

ρ 1

A1

V2

ρ 2

A2

Z1

Z2

Q

Fig. 2: An Incompressible Fluid Flowing Through a Pipe.



F5-13

A1

V1

A2

V2

Fig. 3: A Sudden Expansion.

A1

V1

A2

V2

Fig. 4: A Sudden Contraction.



Fig. 5: Pressurized Piezzometer Tubes to measure Pressure Loss between

two points at different elevations.

P1

P2

2

1Air at

Pressure

x

y

z

Fi 6 U T b t i i d t

O O

x

y

Mercury

Water

2 1

P2 P1

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