A landscape architect is planning an artificial waterfall in a city park. Water

Question

A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.47 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.85 m high, and from there the water falls into a pool (see figure). Will the space behind the waterfall be wide enough for a pedestrian walkway? (Assume that the average pedestrian walkway is 1 m wide.) To sell her plan to the city council, the architect wants to build a model to a scale, which is one-fifteenth actual size. How fast should the water flow in the channel in the model?

Explanation / Answer

A) horizontal distance the water travels is x = u*sqrt(2*h/g) = 1.47*sqrt(2*3.85/9.81) = 1.3 m which is greater than 1m

So the answer is yes

B) now = x = 1.3 m

h = (1/5)*3.85 = 0.77 m

then x = u*sqrt(2*h/g)

1.3 = u*sqrt(2*0.77/9.81) =u*0.396

u = 1.3/0.396 = 3.28 m/s

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