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Water Tunnel Height Experiment

    In order to verify the equation derived here, an experiment was preformed in a water tunnel of 6" width over a wide variety of depths. The volume flow rate, the height of the barrier, and the initial height of the flow were all known

The variables are defined as follows:


Q - volumetric flow rate of the water tunnel

H0 - height of barrier

H - height of the raised water level due to the barrier


Below are photos of the experiment being conducted in the water tunnel

#1

Q = 227.7in3/s          D = 3.125”          H0 = 2.625”          W0 = 6”          H = 4.5”          Ha = 0.75”



#2

Q = 227.7in3/s          D = 3.125”          H0 = 4”          W0 = 6”          H = 5.75”          Ha = 0.5”



#3

Q = 196.7in3/s          D = 4.5”          H0 = 2.625”          W0 = 6”          H = 4.75”          Ha = 3”






#4

Q = 196.7in3/s          D = 4.5”          H0 = 4”          W0 = 6”          H = 5.75”          Ha = 0.75”







#5

Q = 245.9in3/s          D = 4.5”          H0 = 4”          W0 = 6”          H = 5.75”          Ha = 0.75”





The table below tabulates the results and provides a calculation of the percent error between the H measured experimentally to the H calculated by solving the equation derived on this page.




 

Depth before barrier is in place

Q

 

(in3/s)

H0

H

measured experimentally

 

H

calculated through equation

error

1.

3.125”

227.7

2.625”

4.5”

4.11”

9%

2.

3.125”

227.7

4.0”

5.75”

5.49”

5%

3.

4.5”

196.7

2.625”

4.75”

3.97”

16%

4.

4.5”

196.7

4.0”

5.75”

5.37”

7%

5.

4.5”

245.9

4.0”

6.0”

5.58”

7%




    The errors on the height terms is relatively small, so the equation used to calculate the change in height was verified in this experiment.


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