A water pipe must deliver at least 10 litres per second to a water tank on a property on the outskirts of a country town. The pipe will have to be 2 km long, and is fed by the town water supply which delivers a pressure difference of 100 000 Pa. What is the minimum radius this pipe needs? The viscosity of water is 0.001 Pa s.
A) 1.0 cm
B) 1.6 cm
C) 3.5 cm
D) 2.7 cm
E) 15 cm
ANS

Question

Quizplus · Accepted Answer

We can use the Poiseuille's law to solve this problem:

Q = (πr^4ΔP)/(8ηl)

Where Q is the flow rate, r is the radius of the pipe, ΔP is the pressure difference, η is the viscosity of the fluid and l is the length of the pipe.

We want to find the minimum radius, so we need to rearrange this equation to solve for r:

r = [(8ηlQ)/(πΔP)]^(1/4)

Substituting the given values, we get:

r = [(8 x 0.001 x 2000 x 10)/(π x 100000)]^(1/4)

r = 0.027 m = 2.7 cm

Therefore, the minimum radius this pipe needs is 2.7 cm, which is option D.

A Water Pipe Must Deliver at Least 10 Litres Per