Question

Firefighters are holding a nozzle at the end of a hose while trying to extinguish a fire. If the nozzle exit diameter is 8 cm and the water flow rate is 12 m3/min, determine (a) the average water exit velocity and (b) the horizontal resistance force required of the firefighters to hold the nozzle.

Answer 1

Answer:

Answer for the question is given in the attachment.

Explanation:

Answer 2

The velocity of water and the force required to hold the nozzle is required.

The exit velocity is $39.79\ \text{m/s}$

The force required is $7958\ \text{N}$

$\rho$ = Density of water = $1000\ \text{kg/m}^3$

d = Diameter = 8 cm

r = Radius = 4 cm

V = Volume flow rate = $12\ \text{m}^3/\text{min}$

Velocity is given by

$v=\dfrac{V}{A}\\\Rightarrow v=\dfrac{12}{\pi 0.04^2}\\\Rightarrow v=2387.32\ \text{m}^3/\text{min}\\\Rightarrow v=\dfrac{2387.32}{60}\\\Rightarrow v=39.79\ \text{m/s}$

Mass flow rate is

$m=\rho V\\\Rightarrow m=1000\times \dfrac{12}{60}\\\Rightarrow m=200\ \text{kg/s}$

Force is given by

$F=mv\\\Rightarrow F=200\times 39.79\\\Rightarrow F=7958\ \text{N}$

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