Question 5 The figure shows two sections of an old pipe system that runs through

Question

Question 5 The figure shows two sections of an old pipe system that runs through a h ill, with distances dA = dB = 27.0 m and D = 95.0 m. On each side of the h ill, the pipe radius is 1.90 cm. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the left and right sections at 2.10 m/s. Then they release a dye in the water at point A and find that it takes 76.0 s to reach point B. What is the average radius of the pipe within the hill?

Explanation / Answer

here,

radius of pipe , r = 1.9 cm

r = 0.019 m

let the speed in the hill be v

speed in the left and right pipe , vl = 2.1 m/s

therefore,

2*27m/2.1m/s + ( 95m - 2*27m) /v = 76 s

v = 0.82 m/s

let the average radius of the pipe in the hill be r'

using equation of continuity

Area * vl = area at hill * v

pi*r^2 * vl = pi * r'^2 * v

0.019^2 * 2.1 = r'^2 * 0.82

r' = 0.0304 m

r' = 3.04 cm

the average radius of the pipe at the hill is 3.04 cm

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