Fluid Mechanics White Seventh ed Chapter 6 Summary

7/18/2019 Fluid Mechanics White Seventh ed Chapter 6 Summary

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CHAPTER 6

1

Always State Assumptions!!!Possible Assumptions:

Laminar flow (fully developed)

Turbulent flow

Fully developed

Incompressible (Poiseuille) pipe flow

Atmospheric pressure (at where ever)

Negligible velocity (Very large tank draining)

Subsection Summaries

6.1 Reynolds Number Regimes

= =

≈2300

=

=

Viscosity values usually around 1 × 1 0−

6.2 Internal vs. External Viscous Flows

= (

)

Laminar Flow: ≈0.06

For Turbulant Flow:

1.6 ⁄ For Re≤107

6.3 Head Loss – The Friction Factor

ℎ =

2 = 8



CHAPTER 6

2

6.4 Laminar Fully Developed Pipe Flow

= 64

Flow direction is in direction of falling HGL

= +

= +

Compare and if > the flow is from 1 to 2.

Generalized complete incompressible steady flow energy equation:

( +

2 + )

= ( +

2 + )

+ ℎ ℎ + ℎ

Single Pipe Flow Problems

Known Flow Rate:1. Use known flow rate to determine Reynolds number

= =

=

2. Identify whether flow is laminar of turbulent

Laminar < 2300 < Turbulent

3. Use correct expression to determine friction factor

Laminar

=

Turbulent ← (Read off of Moody)

4. Use definition of ℎ to determine friction head loss

ℎ =

2

5. Use general energy equation to determine total pressure drop

(

+

2 + )

= (

+

2 + )

+ ℎ ℎ + ℎ



CHAPTER 6

3

Unknown Flow Rate

1. Assume infinite Reynolds Number

2.

Obtain friction factor as function of roughness only

← (Read off of Moody)

3. Obtain first guess of velocity based on energy conservation

4. Update Reynolds number

5. Update friction factor based on Reynolds number and

EXAMPLE: Chapter 6 Lecture Notes slide 11 on p.6

After equation for V is derived: = √ . ………… (1)

For Reynolds number

=50000 ………… (2)

Initial to determine search line:

=.

=0.002

Assume fully turbulent: → ∞ ← 0.002 ∴ = 0.0235

The assumption of fully turbulent flow is to get initial

1. Insert into eqn. (1) to get new

∴ = 1 . 4 5 9

2. Insert new into eqn. (2) to get new

3. Look up new

on predetermined 0.002

line to determine new

4.

Repeat steps 1 to 3 until is stable



CHAPTER 6

4

Unknown Diameter:

Example 6.10

Find functions that define the diameter of the pipe. In this example:

=

to ≈0.655/

=

to

=

= 6 × 1 0−

1. Guess

2. calculate

3. use to calculate and

4. use

and

to find new

5. Repeat steps 1 to 4 until becomes stable



CHAPTER 6

5

Minor or Local Losses in Pipe SystemsSee Example 6.16

∆ℎ = ℎ + ∑ ℎ = 2 ( + ∑ )

When flow is exiting a pipe to a large reservoir (submerged exit): K =1 ALWAYS!!!!!

Other values for the resistance coefficient k can be read of various graphs in section 6.9 (Minor of

Local Losses in Pipe Systems).

Fig 6.18a: Recent measured loss coefficients for 900 elbows (p.401)

Fig 6.18b: Average loss coefficients for partially open valves (p.402)

Fig 6.20: Resistance for smooth-walled 450, 90

0 and 180

0 bends At Re = 200 000.

Fig 6.21 a & b: Entrance and exit loss coefficients

Fig 6.22: Sudden expansion and contraction losses

Fig 6.23: Flow losses with gradual conical expansion

Sudden expansion:

= 1 =

/

Sudden Contraction:



CHAPTER 6

6

≈0.42 1

Multiple Pipe Systems

Ugh… read p.407 to p.413

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Fluid Mechanics White Seventh ed Chapter 6 Summary