FLUID MECHANICS
EXPERIMENT NO. 6 “TO DETERMINE THE HYDRAULIC CO-EFFICIENT OF GIVEN ORIFICE”
APPARATUS: Hydraulic bench Orifice (Dia 8mm and 5mm) Stop Watch Measuring scale Hook Guages OBJECTIVE: Co-efficient of Velocity Co-efficient of Discharge Co-efficient of Contraction RELATED THEORY: ORIFICE: It is an opening on vertical side or at the base of the vessel. These are used to measure the discharge through container or vessel. In common practice orifice in vertical sides are used.
TYPES OF ORIFICE: There are many types of orifice depending upon shape, size etc.
W.R.T SIZE BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
SMALL ORIFICE: An orifice which is D less than H/5. Velocity almost remains same.
LARGE ORIFICE: An orifice for which D is greater than H/5. In this case velocity varies along the depth.
W.R.T SHAPE Circular shape Rectangular shape Square shape Triangular shape W.R.T NATURE OF THE DISCHARGE: Simple orifice Partially submerged orifice Fully submerged orifice
W.R.T EDGE OR SHAPE BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
Bell mouth orifice Sharp edge orifice JET OF WATER: It is continuous stream of water flowing out of orifice.
VENA CONTRACTA:
It is section of jet of water at which streamlines become parallel. It is also known as min section of water, normally it occurs at d/2 distance from the surface of orifice. Where d is the dia of orifice and at Vena Contracta velocity is max, area is low and dia is minimum.
Q = Cd AO(2gH)1/2 Cd = Q / AO(2gH)1/2 AO = Q / Cd (2gH)1/2 g = (Q / CdAO)2 / 2H H = (Q / CdAO)2 / 2g
Solve for flow rate Solve for Discharge coefficient Solve for orifice area Solve for gravitational constant Solve for centre line head
COEFFICIENT OF HYDRAULIC: It is the ratio of actual velocity of jet at vena contracta and theoretical velocity. Avg. value = 0.97 CV = VACT / VTH Vact = (gx2/2y)1/2 Vth = (2gH)1/2
COEFFICIENT OF CONTRACTION: It is the ratio of area of jet at vena contracta and actual area of orifice. Avg. value = 0.64 CC = Actual cross sectional area / Geometric cross sectional area
COEFFICIENT OF DISCHARGE: BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
It is the ratio of actual discharge and theoretical discharge through the orifice. Avg. value = 0.6 - 0.64 Cd = Qact / Qth Where Qth = ( 2gH)1/2
EXPERIMENTAL RELATION B/W CC, CD, AND CV: Cd = C c x Cv
DETERMINATION OF COEFFICIENT OF DISCHARGE OF VELOCITY BY EXPERIMENT: CV may be found experimentally for an orifice by measuring horizontal and vertical distance as shown in figure. Y = Y’ - YO X = X – d/2 Consider a tank containing liquid and an orifice in one of its vertical side. Let H = Head causing flow V = Horizontal velocity Jet of liquid has a Horizontal velocity v and it is acted upon by gravity with a own word acceleration “g”. Consider a particle p in the jet if t = time taken by the partial to flow from section CC to point p then X=vxt V = distance / t T=x/v Y = ½ gt2 S = v x t + ½ at2 Y = no vertical velocity + ½ gt2 Y = ½ gt2 Equating equation we have Y = ½ g (x/v)2 V2 = gx2/2y Vact = {[gx)2 / 2y} 1/2 Vth = (2gh) 1/2
PROCEDURE: Place the orifice apparatus on the hydraulic bench. Connect the inlet of the apparatus to the outlet of the hydraulic bench. BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
Note the dimensions of the discharge measuring tank, orifice. Check that the zero of the scale of the inlet tank is same level as the centerline of the
mouthpiece or orifice. Adjust the opening of the inlet valve till the water in the supply tank becomes steady. Note down the head. Using the hook guage arrangement measure the co-ordinates of the jet in a convenient point. Using collecting tank and stop watch setup measure the actual discharge. Repeat the experiment for different inlet valve opening and tabulate the readings.
OBSERVATIONS AND CALCULATIONS: H = Head causing flow V = Horizontal velocity For Diameter of Orifice = 5mm Sr. No
Vol.
Time
H
X’
Y’
X=
Y=
Vact=(g
Vth=(
Qact=
Qth=
Cv=
Cd=
C
X’-d/2
Y’-2
x2/2y)1/2
2gh)1/2
V/T
A(2gh)1/2
Vact/
Qact/ Qth
C
Vth
1 2
m3
sec
m
0.00 5
26.9
0.00 5
21.9
m
m
m
m
m/sec
0.27 0.1 3
0.0 7
0.128
0.068 1.0830
0.29 0.1 3
0.0 8
0.131
Y’
X=
Y=
Vact=(g
X’-d/2
Y’-2
x2/2y)1/2
C
m/sec
m3/sec
m3/sec
2.318
1.85x
4.5x10-5
0.467
4.09
8.
2.27x
4.7x
0.759
0.83
6.
10-4
10-5
Vth=(
Qact=
Qth=
Cv=
Cd=
C
2gh)1/2
V/T
A(2gh)1/2
Vact/
Qact/ Qth
C
1.74
3.
10-4 0.027 1.8195
2.398
For Diameter of Orifice = 8mm Sr. No
Vol.
Time
H
X’
Vth 3
1
m
sec
m
0.00 5
23.8
0.25 0.1 4 3
BSCE 01133012
m
m
m
m
m/sec
0.0 7
0.126
0.068 1.0780
THE UNIVERSITY OF LAHORE
3
m/sec
m /sec
m /sec
2.232
2.10x
1.2x10-4
10-4
C
3
0.482
FLUID MECHANICS
2
0.00 5
21.0 6
0.25 0.1 9 3
0.0 8
0.129
0.029 1.6776
5.08
2.37x
2.5x
10-4
10-4
0.33
COMMENTS: Both theoretical and experimental values were calculated for the hydraulic coefficient of the orifice. Orifice of different diameters has been used. And we saw that one with the smaller dia gave larger values of hydraulic coefficient. Experimental values are less than the theoretical values due to the frictional losses. There was some error too that was because the hydraulic bench was repaired. Hydraulic coefficient of orifices is actually the percentage and is calculated as percentage. Then check the zero of the scale of the inlet tank is at same level as the centerline of the mouthpiece. And proper connections are made with the hydraulic bench.
EXPERMENT NO. 7 “TO MEASURE DISCHARGE IN OPEN CHANNEL USING RECTANGULAR NOTCH, CALIBERATE AND MEASURE CO-EFFICIENT OF DISCHARGE”
APPARATUS:
Notch Hydraulic Bench Hook Gauge Stop Watch
BSCE 01133012
THE UNIVERSITY OF LAHORE
0.93 44
2.
FLUID MECHANICS
RELATED THEORY: CO-EFFICIENT OF DISCHARGE: It is the ratio of actual discharge to the theoretical discharge.
HOOK GAUGE: It is used to measure depth of water in open channel.
NOTCH: A standard device used to measure discharge in open channels. It is metallic plate having a regular shape cut.
TYPES OF NOTCHES: Rectangular Notch Triangular Notch Stepped Notch Trapezoidal Notch
DERIVATION: dQth = Vth dA Vth = (2gh)1/2 dA = dh.2x tan (0/2) = x/(H-h) x
= (H-h) tan (0/2)
dA = dh 2(H-h) tan (0/2) dQth = 2(2gh)1/2 (H-h) tan (0/2)dh K’
= 2(2g) 1/2 tan (0/2)
dQth = K’ (h)1/2 (H-h)dh Qth= K’ (4/15)(H)5/2 BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
PROCEDURE: Start discharge of water in rectangular notch and wait till water attains constant level in
notch. Insert hook gauge in it and note it down. Note time of collection for certain volume of water in hydraulic bench. Calculate actual discharge Qth and Cd. Plot graph between Qth and Qact with Qth at x-axis and H at y-axis.
OBSERVATIONS AND CALCULATIONS: m0.5/sec
K= VL =
OBSERVATION
H (mm)
(m)
T
Qact=VL/t
Qth = KH5/2
(sec)
(m3/sec)
(m3/sec)
1. 2. 3. 4.
GRAPHS:
COMMENTS: EXPERMENT NO. 8
BSCE 01133012
THE UNIVERSITY OF LAHORE
Cd
FLUID MECHANICS
“TO MEASURE DISCHARGE IN OPEN CHANNEL USING TRIANGULAR NOTCH, CALIBERATE AND MEASURE CO-EFFICIENT OF DISCHARGE”
APPARATUS:
Notch Hydraulic Bench Hook Gauge Stop Watch
RELATED THEORY: CO-EFFICIENT OF DISCHARGE: It is the ratio of actual discharge to the theoretical discharge.
HOOK GAUGE: It is used to measure depth of water in open channel.
NOTCH: A standard device used to measure discharge in open channels. It is metallic plate having a regular shape cut.
BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
TYPES OF NOTCHES: Rectangular Notch Triangular Notch Stepped Notch Trapezoidal Notch
DERIVATION: dQth = Vth dA Vth = (2gh)1/2 dA = dh.2x tan (0/2) = x/(H-h) x
= (H-h) tan (0/2)
dA = dh 2(H-h) tan (0/2) dQth= 2(2gh)1/2 (H-h) tan (0/2)dh = 2(2g)1/2 tan(0/2)
K’
dQth= K’ (h)1/2 (H-h)dh Qth = K’ (4/15)(H)5/2
PROCEDURE: Start discharge of water in triangular notch and wait till water attains constant level in
notch. Insert hook gauge in it and note it down. Note time of collection for certain volume of water in hydraulic bench. Calculate actual discharge Qth and Cd. Plot graph between Qth and Qact with Qth at x-axis and H at y-axis.
OBSERVATIONS AND CALCULATIONS:K=
m0.5/sec
BSCE 01133012
THE UNIVERSITY OF LAHORE
FLUID MECHANICS
VL =
OBSERVATION
H (mm)
(m)
T
Qact=VL/t
Qth = KH5/2
(sec)
(m3/sec)
(m3/sec)
1. 2. 3. 4.
GRAPHS: COMMENTS:
BSCE 01133012
THE UNIVERSITY OF LAHORE
Cd