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Lab 1: Blue Flume Hydraulic Jump

— David Wagner 2007/10/29 12:17 

Subject: Lab Experiment Skip to message content
Message no. 4
Author: Richard H French
Date: Friday, October 26, 2007 10:41am
All
It appears and sounds like we had a successful experiment last night.  Now what we 
need to do is analyze the data and prove the equation.  I am not expecting a lot of 
words.  For example, a table with the lab data (and units) and then a spreadsheet (or 
other method) analysis of that data.  Final product likely would be a graph - here is 
where you need to think; that is, how do you want to present your final results.  There 
are a variety of valid ways you could do this - you pick what you like and tell me why 
you like it.

Please get this in Tuesday evening

Regards
RHF

Data Collected

  • Slope: 1%, width b=1 ft
ParameterUnitsSymbolData Set 1Data Set 2Data Set 3
Measured Values
Pump 1 Manometerft-H2OΔ1 2.55-1.30 = 1.25 1.98-0.78 = 1.20 1.98-0.78 = 1.20
Pump 2 Manometerft-H2OΔ2 — 2.09-1.09 = 1.00 1.96-1.36 = 0.60
Upstream Depthfty1 0.843 in = 0.0703 1.14 in = 0.0950 1.13 in = 0.0942
Downstream Depthfty2 1.9415 in = 0.162 3.87 in = 0.266 2.78 in = 0.232
Tailgate Heightft — 2 in = 0.17 2.5 in = 0.21 2.2 in = 0.18
Derived Values
Pump 1 Flowft³/sQ1 0.235 0.227 0.227
Pump 2 Flowft³/sQ2 — 0.210 0.162
Total Flowft³/sQ 0.235 0.437 0.389
Froude Number Squared— F1² 5.00 6.92 5.66
Experimental y2/y1ft/ft 2.31 3.39 2.46
Predicted y2/y1ft/ft 2.70 3.25 2.90
Predicted y2ft 0.189 0.309 0.273

Sample Calculations

  1. y_2/y_1 = {sqrt{1+8{F_1}^2}-1}/2 = {sqrt{1+8*5.00}-1}/2 = 2.70
  2. y_2/y_1 = {sqrt{1+8{F_1}^2}-1}/2 = {sqrt{1+8*6.92}-1}/2 = 3.25
  3. y_2/y_1 = {sqrt{1+8{F_1}^2}-1}/2 = {sqrt{1+8*5.66}-1}/2 = 2.90

Results

JpGraph Table Data Plot JpGraph Table Data Plot

The predicted downstream depth is consistently higher than the measured depth by about 17%.

Data SetMeasured y2 (ft)Predicted y2 (ft)Predicted/MeasuredLinear Correlation: 1.17(measured y2)
1 0.162 0.189 1.170.190
3 0.232 0.273 1.180.271
2 0.266 0.309 1.160.311

Perhaps this is because the flume slope adds a little energy so the water flows a bit faster and shallower than expected. It may be worthwhile to get a few more data points to check this relationship holds, then try varying the slope slightly to see if it changes.

This also suggests it may be a good idea to record the distances of the measurement locations and of the jump itself.

Discussion


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