Question

There are 3 inlet pipes whose diameters are 1m, 2m and 3m respectively. if the rate of flow is directly proportional to the square of the diameter, find the time taken to fill an empty tank when all the 3 pipes are opened given that the smallest pipe takes 9 mins to fill the tank?

Answer 1

In 23/6 minutes all pipes will fill the tank

Answer 2

Answer:

Let x be the time taken to fill an empty tank when all the 3 pipes are opened

The rate of flow is directly proportional to the square of the diameter

Rate of flow of 1 m pipe = 1m/min

The smallest pipe takes 9 mins to fill the tank

Amount flow in x min = $\frac{x}{9}$

Rate of flow of 2 m = 4 m /min

Amount of flow in x min = 4x

Rate of flow of 3 m = 9 m /min

Amount of flow in x minute = 9x

ATQ

$1 \times \frac{x}{9}+4(4x)+9(9x)=1$

$x=\frac{9}{874}$