Title
Study the effect of sluice gate on the flow of fluid in a rectangular channel
Objectives
1. Learn the basic theory of flow under sluice gate in a rectangular channel
2. Using momentum function consideration to find force exerted on flow by the sluice gate
3. Calculate the power loss and energy head loss at jump suction using specific energy consideration
Introduction
According to Dr. Khalil M. ALASTAL (n.d) an open channel is like a duck with flowing fluid and whose surface is exposed to atmosphere. As the atmospheric pressure remains constant through the length of duct so the fluid flows only due to the difference in potential energy.
Sluice gate is the device used to control the flow of fluid and also for measurement of discharge rate in an open channel. It can move vertically up and down or rotate about a point to restrict the flow of water.
According to R. V. RAIKAR (n.d) fluid flowing in a channel always has the momentum function M and specific energy E and both of these quantities can be calculated by using following formula
M= q^2/gy+ y^2/2
E=y+ q^2/(2gy^2 )
In above equation y is depth of the flow, g is the gravitational acceleration and q is the ratio of quantity of flow also called flow rate to width of channel.
Applying the concept of specific energy and momentum function on the flow under the sluice gate with formation of hydraulic jumps gives
Flow under the sluice
E_1= E_2
p/ρg= M_2 M_1
Here first equation show the zero energy losses and in second equation p is the force per unit width applied on the fluid by the sluice gate, ρ is the density of the fluid, M_2 is the momentum function at point 2 and M_1 is the momentum function at point 1.
For the Hydraulic Jump
M_2= M_3
y_3= y_2/2 ×( √(1+8F_r2^2 )1)
Where F_r2is the Froude number at the section 2.
F_r2=q/√(gy_2^3 )
If the energy losses is represented by dE then
dE= E_2 E_3
Power losses due to the jump can be calculated as follow
Power Losses= ρ ×g ×Q ×dE
Procedure
According to Dr. Khalil M. ALASTAL (n.d)
1. Set up the flow channel apparatus
2. Adjust the support frame feet so that the flow channel does not rock
3. Reset the clock dial to zero
4. Note dial counter gauge reading
5. Check the water depth along the length of channel, it should be constant to prove that the slope of bed is zero
6. Position the sluice gate at the height of 37mm from the bed of channel
7. Seale the side between the sluice gate and channel wall to ensure zero leakage
8. Note down the width of channel
9. Start supplying water in to the channel
10. Use flow control valve and downstream wire to get the required profile of flow
11. Let the flow to be steady before start measuring the value of flow rate and three depths y_1,〖 y〗_2 and y_3
Results
Numbers of experiments were performed according to above mention procedure, with different flow rates and data was recorded in the following table.
Table
1 Experimental Data
b (m)

Q ()

y1 (m)

y2 (m)

y3 (m)

q ()

0.08

0.00093

0.167

0.0082

0.0515

0.011625

0.08

0.00084

0.1355

0.0082

0.0506

0.0105

0.08

0.00072

0.1005

0.0082

0.0288

0.009

Following table were generated by using the formula for the
specific energy E and momentum function M
M= q^2/gy + y^2/2
E=y+ q^2/(2gy^2 )
Table
2 Calculated Values of E and M
E1 (m)

E2 (m)

E3 (m)

M1

M2

M3

1.68E01

1.11E01

5.15E02

1.40E02

0.00171531

1.59E03

1.36E01

9.19E02

5.06E02

9.18E03

0.001405571

1.50E03

1.01E01

6.97E02

2.88E02

5.05E03

0.001041584

7.02E04

Following formulas
where used to calculate the difference in energy, forced applied per unit
width, force exerted by gate of flow F and Power Losses
dE= E_1 E_2
dE= E_2 E_3
p/ρg= M_2 M_1
F=p ×b
Power Losses= ρ ×g ×Q ×dE
Table
3 Calculated Value of Energy and Power Loss
Energy Loss E12 (m)

Energy Loss E23 (m)

P (N/m)

Force exerted my gate of flow F (N)

Power Loss (W)

5.68E02

5.92E02

1.20E+02

9.63E+00

5.40E01

4.40E02

4.13E02

7.62E+01

6.10E+00

3.40E01

3.12E02

4.09E02

3.93E+01

3.14E+00

2.88E01

Using the following equation obtain by applying the condition that energy loss due to friction is zero that is E1 = E2 to calculate the y1 value by using the measured value of y2
y_1= 〖2y〗_2/(1+√(1+ (〖8gy〗_2^3)/q^2 ))
Table
4 Calculate
value for y1
y2 (m)

y1 (m)

0.0082

0.110174

0.0082

0.091179

0.0082

0.068788

Using the following equation obtain by applying the condition that energy loss due to friction is zero that is M1 = M2 to calculate the y3 value by using the measured value of y2
y_3= y_2/2 + ( √(1+8 × F_r2^2 )1)
Table
5 Calculate value for y3
y2 (m)

y3
(m)

0.0082

0.054039

0.0082

0.048442

0.0082

0.040986

Discussion
We have two values of y1 for each value of flow rate. One is the measured value and other is the calculated value. Calculated value of y1 is less than the measure value of it this is because the calculated value was taken by consideration that friction is zero and measured value was taken when friction was present. Friction will stop water to pass through the gate so that’s why measured y1 is higher.
We also have two values of y3 for each value of flow rate. One is the measured value and other is the calculated value. Calculated value of y3 is greater than the measure value of it this is also because friction. Friction will stop water to pass through the gate so that’s why measured y3 is less
Conclusion
• Net specific energy of flowing water decrease due forces exerted by the gate which lower the depth of water
• Net specific force of flowing water also decrease this also due to lower value of depth due to gate forces
• Friction has some effect of the depth of water and so on the energy and power losses
• Measured value of depth is greater than the calculated one before the gate
• Measure value of depth is lesser than the calculated one after the gate
References
• Dr. Khalil M. ALASTAL (n.d) Fluid Mechanics Lab Experiment 13 [online] Available (http://site.iugaza.edu.ps/mymousa/files/Experiment134hydraulicslab2.pdf )
• By R. V. RAIKAR (n.d) Experiment 6.7 hydraulic jump, LABORATORY MANUAL HYDRAULICS AND HYDRAULIC MACHINES.
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