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 1.60 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.75 m high, and from there the water falls into a pool (see figure). (a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (Assume that the average pedestrian walkway is 1 m wide.) Yes No (b) To sell her plan to the city council, the architect wants to build a model to a scale, which is one-seventeenth actual size. How fast should the water flow in the channel in the model? Your response differs from the correct answer by more than 10%. Double check your calculations. m/s

Explanation / Answer

a)time taken to reach ground=sqrt(2h/g)=sqrt(2*3.75/9.8)=0.875s

Horizontal distance travelled = 0.875*1.6 =1.4m

This is greater than 1m. Therefore, pedestrian will be able to cross

b) when the model has to be made in one-seventeenth of actual size, the height of waterfall=3.75/17=0.220m

The distance between wall and waterfall=1.4/17=0.082m

The horizontal velocity in model has to be such that height of fall=0.220 and distance between wall and fall is 0.082m

Time taken by waterfall =t= 0.082/v

0.22 = (1/2)*9.8*(0.082/v)²

v=0.387 m/s

Therefore, in model the water should flow at 0.387 m/s

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