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 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.55 m high, and from there the water falls into a pool.

(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 or no)

(b) To sell her plan to the city council, the architect wants to build a model to a scale, which is one-fourteenth actual size. How fast should the water flow in the channel in the model?

Explanation / Answer

Given horizontal velocity of water = 1.7m/s

Height of water fall = 3.55

So time taken to hit the pool is h = 0.5gt^2

So 3.55 = 4.9t^2

So t = 0.85 seconds.

Therefore range of fall of water fall, i.e horozontal distance of the fall is 1.7m/s * 0.85 seconds = 1.445m

So waterfalls away from pedestrian walkway so space is enough

(b)

The scale is 1/14 th of size. So height of model is 3.55/14 m and walkway is 1/14 m

So height is 0.253 m and 0.07m walkway.

Now h = 0.5gt^2

So time = 0.22 seconds

So horizontal distance must be greater than 0.07m so let waterflow speed is v

we have v* 0.22 = 0.07

So v = 7/22 m/s which is 0.32 m/s

So speed of flow must be more than 32cm/s

So t =

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