A spillway model is to be built to a scale of 1:25 across a flume that is 2 ft wide. The prototype is 37.5 ft high, and the maximum head expected is 5.0 ft. (a) What height of model and what head on the model should be used? (b) If the flow over the model at 0.20 ft head is 0.70 cfs, what flow per

Question

A spillway model is to be built to a scale of 1:25 across a flume that is 2 ft wide. The prototype is 37.5 ft high, and the maximum head expected is 5.0 ft. (a) What height of model and what head on the model should be used? (b) If the flow over the model at 0.20 ft head is 0.70 cfs, what flow per ft of prototype can be expected? (c) If the model shows a measured hydraulic jump of 1.0 in, how high is the jump in the prototype? (d) If the energy dissipated in the model at the hydraulic jump is 0.15 horsepower, what would be the energy dissipation in the prototype?

Accepted Answer

(a) Since [latex]\frac{length in model}{length in prototype} =\frac{1}{25} [/latex], height o f model [latex]\frac{1}{25} imes 37.5=1.5 [/latex] ft and

head on model [latex]=\frac{1}{25} imes 5.0=0.20 [/latex] ft.

(b) From Problem 6.18, [latex]Q_{r}=L^{5/2}_{r} [/latex] , since gravity forces predominate; then

[latex]Q_{p}=\frac{Q_{m}}{L^{5/2}_{r}}=(0.70)/(1/25)^{5/2}=2188 [/latex] cfs

This quantity can be expected over 2 x 25 or 50 ft of length of prototype. Thus the flow per ft of prototype = 2188/50 = 43.8 cfs.

(c) [latex]\frac{h_{m}}{h_{p}}=L_{r} [/latex] or [latex]h_{p}=\frac{h_{m}}{L_{r}}=\frac{1.0}{1/25}=25 [/latex] in (height of jump)

(d) Power ratio [latex]P_{r}=(ft-lb/sec)_{r}=\frac{F_{r}L_{r}}{T_{r}}=\frac{\gamma _{r}L^3_{r}L_{r}}{\sqrt{L_{r}/g_{r}} } [/latex] . But [latex]g_{r}=1 [/latex] and [latex]\gamma _{r}=1 [/latex] .Then

[latex]\frac{P_{m}}{P_{p}}=L^{7/2}_{r}=\left(\frac{1}{25} ight)^{7/2} [/latex] and [latex]P_{p}=P_{m}(25)^{7/2}=(0.15)(25)^{7/2}=11,700 [/latex] hp

Question 6.30: A spillway model is to be built to a scale of 1:25 across a ...

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