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:

a) the average water exit velocity is 39.79m/s

b)the horizontal resistance force required of the firefighters to hold the nozzle is 7958N

Explanation:

Given that,

The exit diameter of the nozzle, D = 8cm = 0.08m

The volume water flow rate, Q = 12m³/min = 0.2m³/s

Density of water is 1000kg/m³

a)

$V = \frac{Q}{A}$

A = πd²/4

 = π(0.08)²/4

 = 5.03 × 10⁻³m₂

$V = \frac{0.2}{5.03\times10^-^3} \\\\V = 39.79m/s$

Therefore, the average water exit velocity is 39.79m/s

b)Calculate the mass flow rate using the equation below

$m=pQ$

where

$p$ is the density of water

Q is the flow rate

m = 1000kg/m³ × 0.2m³/s

m = 200kg/s

Now the momentum equation for steady one dimensional flow

$\sum \bar F=\sum_{out} \beta m \bar V - \sum_{in} \beta m \bar V$

Now the momentum equation along x axis is

$F_{Rx}=mV_{exit}\\\\=(200)\times(39.79)\\\\=7958N$

Therefore, the horizontal resistance force required of the firefighters to hold the nozzle is 7958N

Answer 2

Answer:

Answer for the question is given in the attachment.

Explanation: