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 = ?

Answer:

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

The force exerted is 318.86 N

Explanation:

The force exerted by such a stream is calculated by multiplying the mass flow rate of water by the velocity of the stream of water.

mass flow rate = 21.4 kg/s

velocity = 14.9 m/s

Force exerted = 21.4 kg/s * 14.9 m/s = 318.86 kgm/s^2 = 318.86 N