Answer to Question #278758 in Astronomy | Astrophysics for Gingging

Question

1. Calculate the pressure needed for the pump of a 3 cm radius fire hose to pump water through

its nozzle of radius 2 cm at an average speed of 4 m/s when the nozzle is 15 m above the fire

track.

Answer 1

Explanations & Calculations

• Hello Gingging,

• This question needs exactly the same procedure that you need to follow in the question you posted under Q278759.
• First use the concept of volumetric flow rate being constant as water is incompressible for the input and output conditions. This helps you find the speed at the input ($\small v_1$ ).

• Once you have found that detail, use the Bernoulli's equation for the input and output conditions to find the pressure at the input.
• But for this case, there is a height between the output and the input that is 15 meters.
• Therefore, the equation includes a variable $\small h$ in addition to that used in the question Q278759.
• For the input,

$\qquad\qquad \begin{aligned} \small P_1+\frac{1}{2}\rho v_1^2+0=\text{constant} \end{aligned}$

• For the output at the given height with respect to the input,

$\qquad\qquad \begin{aligned} \small P_2+\frac{1}{2}\rho v_2^2+\rho g H&=\small \text{constant} \end{aligned}$

• Equal both equations and find the pressure at the input.

• Again, lengths should be converted into meters before substituting to the equations to match the units of speed.