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### Effect of Sluice Gate on the Flow of Fluid Lab Manual

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 1.68E-01 1.11E-01 5.15E-02 1.40E-02 0.00171531 1.59E-03 1.36E-01 9.19E-02 5.06E-02 9.18E-03 0.001405571 1.50E-03 1.01E-01 6.97E-02 2.88E-02 5.05E-03 0.001041584 7.02E-04

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) 5.68E-02 5.92E-02 -1.20E+02 -9.63E+00 5.40E-01 4.40E-02 4.13E-02 -7.62E+01 -6.10E+00 3.40E-01 3.12E-02 4.09E-02 -3.93E+01 -3.14E+00 2.88E-01

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/Experiment-13-4-hydraulics-lab-2.pdf )
By R. V. RAIKAR (n.d) Experiment 6.7 hydraulic jump,  LABORATORY MANUAL HYDRAULICS AND HYDRAULIC MACHINES.