A rectangular pier in a river is 1.22 m wide by 3.66 m long, and the average depth of water is 2.74 m. A model is built to a scale of 1:16. A velocity of flow of 0.76 m/s is maintained in the model, and the force acting on the model is 4.0 N. (d) What are the values of velocity in and force on the

Question

A rectangular pier in a river is 1.22 m wide by 3.66 m long, and the average depth of water is 2.74 m. A model is built to a scale of 1:16. A velocity of flow of 0.76 m/s is maintained in the model, and the force acting on the model is 4.0 N. (d) What are the values of velocity in and force on the prototype? (b) If a standing wave in the model is 0.049 m high, what height of wave should be expected at the nose of the pier? (c) What is the coefficient of drag resistance?

Accepted Answer

(a) Since gravity forces predominate, from Problem 6.19 we obtain

[latex]\frac{V_{m}}{V_{p}}=\sqrt{L_{r}} [/latex] and [latex]V_{p} =\frac{0.76}{(1/16)^{1/2}}=3.04 [/latex] m/s

Also , [latex]\frac{F_{m}}{F_{p}}=\gamma _{r}L^3_{r} [/latex] and [latex]F_{p}=\frac{4.0}{(1.0)(1/16)^3} =16.4 [/latex] kN

(b) Since [latex]\frac{V_{m}}{V_{p}}=\frac{\sqrt{L_{m}} }{\sqrt{L_{p}} } [/latex] , [latex]\sqrt{h_{p}}=\sqrt{0.049} imes \frac{3.04}{0.76} [/latex] and [latex]h_{p}=0.784 [/latex] m wave height.

(c) Drag force [latex]=C_{D} ho A\frac{V^2}{2} [/latex] , [latex]4.0 = C_{D}(1000)\left(\frac{1.22}{16} imes \frac{2.74}{16} ight)\frac{(0.76)^2}{2} [/latex] , and [latex]C_{D}=1.06 [/latex] .

Had the prototype values been used for this calculation, we would have the following:

[latex](16.4)(1000)=C_{D}(1000)(1.22 imes 2.74)\frac{(3.04)^2}{2} [/latex] and [latex]C_{D}=1.06 , [/latex] as expected .

Question 6.32: A rectangular pier in a river is 1.22 m wide by 3.66 m long,...

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