Problem: Suppose that the rate of flow of water through a fire hose is 21.4 kg/s and the stream of water from the hose moves at 14.9 m/s. What force is exerted by such a stream

Given Information:

mass flow rate = 21.4 kg/s

change in velocity = 14.9 m/s

Required Information:

Force = ?

Force = 318.86 N

Explanation:

We know that force is equal to change in momentum over time

F = Δp/t

Where change in momentum is

Δp = m(v₂² - v₁²)

so force becomes

F = m(v₂² - v₁²)/t

Where m/t is basically mass flow rate 21.4 kg/s

F = 21.4 kg/s*(v₂² - v₁²)

The change in velocity is given as

v₂² - v₁² = 14.9 m/s

F = 21.4 kg/s * 14.9 m/s

F = 318.86 kg.m/s²

1 kg.m/s² is equivalent to 1 Newton of force

F = 318.86 N