Question

In riot control, the riot squad uses a water hose that shoots water at a rate of 5 m/s and volume of 30 L/s. What is the average force exerted on a person assuming that the water splashes sideways in all directions? The density of water is 1000 kg/m3.

Answer 1

Answer:

The average force exerted on a person assuming that the water splashes sideways in all directions is 150 newtons.

Explanation:

From Fluid Mechanics and Newton's Laws we know that water stream is an example of a variable mass system at constant speed and the magnitude of the net force done by the water splash ($F$), measured in newtons, is given by the following expression:

$F = \rho\cdot \frac{dV}{dt}\cdot v$ (Eq. 1)

Where:

$\rho$ - Density of water, measured in kilograms per cubic meter.

$\frac{dV}{dt}$ - Volume flow rate, measured in cubic meters per second.

$v$ - Flow velocity, measured in meters per second.

If we know that $\rho = 1000\,\frac{kg}{m^{3}}$, $\frac{dV}{dt} = 0.03\,\frac{m^{3}}{s}$ and $v = 5\,\frac{m}{s}$, the average force exerted on a person is:

$F = \left(1000\,\frac{kg}{m^{3}} \right)\cdot \left(0.03\,\frac{m^{3}}{s} \right)\cdot \left(5\,\frac{m}{s} \right)$

$F = 150\,N$

The average force exerted on a person assuming that the water splashes sideways in all directions is 150 newtons.