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

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

Step-by-step 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 (dV)/(dt)\cdot v` (Eq. 1)

Where:

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

`(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\,(kg)/(m^(3))`,
`(dV)/(dt) = 0.03\,(m^(3))/(s)` and
`v = 5\,(m)/(s)`, the average force exerted on a person is:

`F = \left(1000\,(kg)/(m^(3)) \right)\cdot \left(0.03\,(m^(3))/(s) \right)\cdot \left(5\,(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.