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fluids

Experiment 1 CENTRE OF PRESSURE ON A PLANE SURFACEI. OBJECT To determine the position of the centre of pressure on the rectangular face of the torroid. II. APPARATUS Hydrostatic Pressure Apparatus

III. ANALYSIS Hydrostatic force acting on the rectangular face: P = ghC A I and its center y D = y C + yC A Partial immersion (1) (2)

L

a

y ; A by m hC = y C = Water= surface 2 y

yD

(3) yC d

b

1 gby 2 (4) 2 by 3 y y D y C = 2 12 = (5) 6 by 2 Moment M of P about knife-edge axis is given by: y y 1 M = gby 2 a + d + (6) 2 2 6 y 1 M = gby 2 a + d and then (7) 2 3 Also M = gmL Where m = mass added to balance pan L = distance from knife-edge axis to balance pan suspension rod axis Thereby, y 1 mL = by 2 a + d (8) 2 3 Hence P= Complete immersion hC = y C = y d ; A = bd 2 (9)

Hence

d P = g y bd 2

(10)

L

a Water surface yD y yC d

m

b d2 12 = bd ( y d / 2) 12( y d / 2 ) Moment M of P about knife-edge axis is given by: y D yC = bd3

(11)

d d d2 M = gbd y a + + 2 2 12( y d / 2 ) and thereby, d d2 mL = bd y a + d + 2 12( y d / 2 ) IV. PROCEDURE

(12)

(13)

(a) Locate the torroid on the dowel pins and fasten to the balance arm by the central screw. (b) Measure the dimensions a, b, and d, and the distance L from the knife edge axis to the balance pan axis. (c) Position the perspex tank on work surface and locate the balance arm on the knife edges. (d) Attach a length of hose to the drain cock and direct the other end of hose to the sink. Attach a length of hose to tap V3 and place the free end in the triangular aperture on the top of the perspex tank. Level the tank, using the adjustable feet in conjunction with the spirit level. (e) Adjust the counter - balance weigh until the balance arm is horizontal. This is indicated on a gate adjacent to the balance arm. (f)Fill water to the perspex tank until the water is level with the bottom edge of the torroid. (g) Place a mass on the balance pan and fill water to the tank until the balance arm is horizontal. Note the water level on the scale. Fine adjustment of the water level may be achieved by over filling and slowly draining, using the drain cock. (h) Repeat the procedure under section (g) for different masses : 5 masses for water levels y > d (complete immersion) and 5 masses for y < d (partial immersion) (i) Repeat readings for reducing masses on the balance pan. All record data can be arranged as shown in table 1 and 2 Table 1. a(cm) b( cm) d(cm) L (cm)

Table. 2 Case Complete immersion y>d m (g) y (cm)

Patital immersion y d (complete immersion) 1 d m Tabulate y = y , and y 2 y Plot m 1 against y y

From (13), it is found that the slope of this graph should be bd3/(12L) And the intercept should be d the experimantal results and theory between bd a + L 2 V. CONCLUSIONS Comparision Give reasons for the discrepancies, if any, between the measured and predicted values of the above expressions for the graph parameters.

Experiment 2

FLOW OVER A WEIR

I. THE OBJECTIVES OF EXPERIMENT To investigate the characteristics of flow over a vee notch and a rectangular notch. To determine the velocity coefficient and discharge coefficient. II. EQUIPMENT SET UP

- Hydraulics Bench, Point Gauge, stop watch. - Basic Weir: 1 - Triangular weirs of 900 notch. 2 - Rectangular weirs. III. SUMMARY OF THEORY The discharge flowing over the weir can be determined by formula: Triangular weir 8 2 g tan 5/2 Q=Cd (1) 15 2 Rectangular weir 2 B 2g H 3/2 Q = Cd 3 (2) Where: Cd, Cd : discharge coefficient IV. PROCEDURE

Ensure that the hydraulic bench is located on a level floor, as the accuracy of the results will be affected if the bench top is not level. Set up the equipment as shown in the diagram.B =101mm 900 Triangular weir H H H: Water head on the weir

Rectangular weir Set Vernier Height Gauge to a datum reading, by placing the point on the crest of the weir. Take extreme care not to damage the weir plate with the point gauge. Position the gauge about half way between the notch plate and stilling baffle. Admit water to channel, adjust flow control valve to obtain heads, H, increasing in step of about 1cm. For each flow rate, stabilize conditions, measure and record H. Take reading of volume and time using the volumetric tank to determine the flow rate. Regulate the flow rate over the V - notch by adjusting the control valve of pump. For each flow rate, stabilize conditions, measure (Zb) to determine the head above notch bottom (H), and take reading of volume (V) and time (T) to determine the flow rate. In order to increase the degree of accurate of flow rate measurement, it should be taken at least three sets of reading of volume and time. Replace triangular weir by rectangular weir and repeat procedure above for rectangular weir. All record data can be arranged as shown in Table I. Table I Weir type No. of Experiment 1 Zb (cm) Z cr (cm) Volume (V) (litre) Time (T) (s)

2 Triangular weir 3

4 Table 2

Weir type

No. of Experiment 1

Zb (cm)

Z cr (cm)

Volume (V) (litre)

Time (T) (s)

2 Rectangular weir 3

4 V. REPORT 1. From Table 1, calculate the water head (H) on the weirs and the discharge in each experiment. 2. For the triangular weir: a) Compute and tabulate Q and Q2/5. b) Plot Q2/5 against H. c) Find Cd from the slope of the graph. d) Are Cd, Cd constant for the condition of the flow? e) What are the advantages and disadvantages of plotting Q2/5 against H instead of Q against H5/2. 3. For the rectangular weir: a) Compute and tabulate: 3Q Q,H3/2, Cd = ,Q2/3, log Q, log H 2 2g 3 / 2 b) Plot: - Q 2/3 against log H. - Log Q against log H. - Cd against H. c) Is Cd constant for this weir? Can the Q H relationship be described by an empirical formula Q = KHn, if so, find the values of K and n.

Experiment 3

FRICTION LOSS IN PIPE

I. OBJECTIVES OF EXPERIMENT - To investigate the variation of friction head along a circular pipe with the mean flow velocity in the pipe. - To investigate the friction factor against Reynolds number and roughness. II. EQUIPMENT SET UP

A pipe of 10.64cm diameter is supplied by water a centrifugal pump. Five test sections with interval of 3 m are connected to a bank of pressurized manometer tubes. Water from the pipe flow into the concrete channel, and at the end of channel a vee-notch, is installed to measure the flow rate in the channel, this flow rate is equal to the flow rate in the pipe. Water level over the vee-notch is measured by a point gauge mounted on a small tank which is opened to the channel. The flow rate over the vee-notch is calculated by formula as follow: 8 5 Q = tg CD 2 g .h0 / 2 (1) 15 2 Where: = 90o CD = 0.58 g = 9.81 m/s2 ho = ZCR z Where z is water level, ZCR is the elevation of the crest of Vee-notch, ZCR = 28.335cm The flow rate over the Vee-notch is regulated by a control valve of pump, and an ampere meter mounted on an electric box will show the current intensity of motor corresponding to the flow rate in the pipe. The difference of pressure

between the test sections in the pipe are measured by reading the water level in the water level in the tubes of manometer. III. SUMMARY OF THEORY Considering flow at two sections i,j in a pipe, Bernouillis equation may be written as: V j2 Pj Vi 2 Pi + + Zi = + + Z j + hij (2) 2g 2g Where: Vi, Vj : velocity at section i, j respectively Pi, Pj : pressure at section i, j respectively Zi, Zj : elevation at of water surface section i, j hi,j : friction loss from section i to section j For this apparatus, Zi = Zj, Vi = Vj, hence Pi Pj hi , j = = hi , j (3) hi,j : the difference of manometer reading at section i and section j. On the other hand, the friction factor can be determined by Darcys formula : L V2 hi , j = f (4) D 2g Where : f : friction factor L : the distance between section i and j D : diameter of pipe V : velocity of pipe The friction coefficient depends upon the Reynolds number of flow and upon the ratio e/D, the relative roughness of the pipe. e f = F Re , (5) D Where : Re : Reynolds number Re = VD/ ( : viscosity coefficient) e : size of roughness e : relative roughness D e For a given pipe, is a constant D IV. PROCEDURE 1. Open the control valve (1) to discharge water into pumping chamber. When the pumping chamber is full of water, close control valve (1). 2. Open the valve at the end of the pipe (2). 3. Turn on power to start pump and use the control valve to regulate the flow rate in the pipe according to the current intensity shown in ampere meter. 4. For 3 large flow rates corresponding to current 20A < I < 22A : - Closing the valves on the tubes 3,4 of manometer. - Reading the water level in the tubes 1 and 2, and measuring the water level before the Vee-notch in the channel by point gauge. 5. For 5 flow rates corresponding to current I < 20.5A, repeat the same procedure above. The data table may be arranged as follows :

Table 1 No 1 2 3 1 2 3 4 5 I Amper e 21.5 21 20.5 20 19.5 19 18.5 18 Manometer (1) (2) reading (3) (mm) (4) Water Level (z) (cm)

V. REPORT For 3 large flow rates 1. Compute the flow rates in the pipe from the measured data in table 1. 2. Compute the head loss between section (1) and (2). And then plot the head loss against flow rates. Conclude the relationship between the head loss and flow rates. For 5 small flow rates

3. Determine 7 small flow rates by using the measured data in Table 1. 4. Compute the head loss between sections 2-1, 3-1 and 4-1. And then plot the graph of the friction loss against the distances. Give the conclusions about the relationship between the friction loss and the distances. For 8 flow rates (3 large flo