Question #278758

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.

1
Expert's answer
2021-12-12T16:43:07-0500

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 (v1\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 h\small h in addition to that used in the question Q278759.
  • For the input,

P1+12ρv12+0=constant\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,

P2+12ρv22+ρgH=constant\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.





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