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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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