flow over a rectangular and vee notches
Post on 14-Apr-2015
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ATOOMUS احمد توفيق مؤمنالعتوم
1
OBJECT: To determine and comment on the coefficient of discharge for the Vee and rectangular notches provided.
APPARATUS:
1. Hydraulics Bench2. rectangular weirs 3. vee notch 4. Stop watch.
THEORY:
The theoretical discharge foe the rectangular weir is given by: Qtheo = (2/3) (2g)(1/2). B. H(3/2)
And for vee notch is given by: Qtheo = (8/15). (2g) (1/2) . tan(/2) . H(5/2)
Where B = breadth of rectangular notch H = hight of flow over notch = Angle of vee notch g = Gravitational acceleration
To the contraction of the flow area downstream of the notch, the actual discharge Q is considerably less and may be expressed as: Qact = Cd .(2/3). (2g)(1/2).B. H(3/2)
Where Cd : the coefficient of discharge for the rectangular notch.
And Qact = Cd (8/15). (2g) (1/2) . tan(/2) . H(5/2)
Where Cd : the coefficient of discharge for the vee notch.
ATOOMUS احمد توفيق مؤمنالعتوم
2
PROCEDURE:
1. Slide the stilling baffle into the slots in the sides of the channel. Install the weir plate 4H 0n on the upstream side of the weir carrier and secure it using the thumb nuts.2. position the hook and point gauge, mounted on the instrument carrier, on the side channels adjacent to the weir plate.3.start he pump, and admit water to the channel by opening the flow control valve. Allow the level to rise until water discharge over the weir plate. Close the flow control valve and allow the water level to stabilize. Set the vernier height gauge to a datum reading using the top of hook.4. position the point gauge about half way between the notch plate and the stilling baffle. Admit water to the channel and adjust the flow control valve to obtain heads H increasing in steps of about 1cm.5. For each flow rate allow conditions to become steady, measure and record H and take readings of volume and time using the volumetric tank to determine the flow rate.6. For ach notch obtain five readings of H and Q.
RESULTS:
Breadth of rectangular notch = B = 3 cmApex angle of the vee notch = = 900
CALCULATION AND GRAPHS:
For a rectangular notch Q = K H(3/2)
K = Cd .(2/3). (2g)(1/2).B @ B = 0.03 mVol. m3
x10-
3
TimeSec.
Qact
m3/secx10
-4
Hmm
Qtheo
m3/sec x10
-
4
Cd K Log H Log Q
3 43.5 0.6896
13.6
1.45 0.47558 0.042 -1.8664
-4.16141
3 21.5 1.395 23.5
3.19 0.437 0.0387 -1.6299
-3.85543
10 22.5 4.44 42.5
7.76 0.572 0.05057 -1.3716
-3.3526
10 18.3 5.46 49.8
9.85 0.554 0.04908 -1.3027
-3.2627
ATOOMUS احمد توفيق مؤمنالعتوم
3
15 16.41
9.14 68.7
15.95 0.5392 0.04776 -1.1630
-3.0390
For first reading:
Qact = 0.003/43.5 = 0.00006896 m3/sec Qtheo = (2/3)*(2*9.81) 0.5*0.03*0.01361.5 = 0.000145 m3/secCd = Q/ Qtheo = 0.47558 K = (2/3)x0.03x( 2*9.81) 0.5 x 0.47558 = 0.042 Should be n =~ (3/2 ) →→ if we take the log for the two sides of equation : log Q = log K + n log H , where n : the power of H = the slope.→→→→ ((-4.16141 +3.0390)/( -1.8664+1.1630))= 1.59 from table . log k = -1.2 from graph → k = 0.063 → Cd = 0.711 .
ATOOMUS احمد توفيق مؤمنالعتوم
4
For Vee notch Q = K H(5/2)
K = Cd .(8/15). (2g)(1/2).tan (/2) Vol. m3
x10-
3
TimeSec.
Qact
m3/secx10
-4
Hmm
Qtheo
m3/sec x10
-
4
Cd K Log H Log Q
3 34 0.882 20.1
1.3531
0.6518 1.5392 -1.696 -4.0545
1 61.6 0.162 8 0.135 1.199 2.8335 -2.096- -4.790 ATOOMUS احمد توفيق مؤمن
العتوم 5
23 31.5 0.095
221 1.597 0.0596 0.1408 -1.677 -5.0213
5 63.52
0.787 19 1.1755
0.6695 1.582 -1.721 -4.10
5 37.48
1.33 24 2.108 0.639 1.5096 -1.62 -3.876
5 12.75
3.92 37.3
6.3477
0.618 1.4588 -1.428 -3.407
For a vee notch Q = K H(5/2)
K = Cd (8/15). (2g) (1/2) . tan(/2) For first reading: Qact = 0.003/34 = 0.0000882 m3/secQtheo = (8/15) (2x9.81)0.5 x tan(90/2) (0.00201)2.5 = 0.00013531 m3/sec CD = ( 0.0000882 / 0.000135310 ) = 0.6518 K = CD x (8/15) (2x 9.81) 0.5 x tan(90/2) = 1.5392 Should be n =~ (5/2 ) →→ if we take the log for the two sides of equation : log Q = log K + n log H , where n : the power of H = the slope.→→→→ ((-3.876 +3.407 )/(-1.62 +1.428))= 2.44 from table .
log k = - 0.9 from graph → k = 0.1259 → Cd = 0.0533 .
ATOOMUS احمد توفيق مؤمنالعتوم
6
Conclusion : As we have seen the best lines drawn result werw quite near to the expected result for the ( n ) or the slope values but considering the K value the results were not expected due to the relatively large difference between the drawing interpolation and the calculated values .
Rectangular
0
2
4
6
8
10
020406080
H ( mm )
Q (
m3 /
s )
Note : Krect. < Kvee.
ATOOMUS احمد توفيق مؤمنالعتوم
7
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