Maximum height of pumped water

  • #1

Homework Statement



There is a fire in a building, so the fireman connects a hose to a hydrant that pumps 2 litres of water per second. The exit of the hose has and area of 15cm^2.
Which is the maximum floor of the building that the water can reach considering that it exits the hose at an height of 1,5m from the ground with an angle of 75 degrees?


Homework Equations



The pressure in a fluid at depth h in the fluid: p = Po + dgh
Equation of continuity for fluids: A1.v1 = A2.v2
Bernoulli’s equation: p1 + 1/2dv1^2 + dgh = constant

The Attempt at a Solution



Assuming that the area of the exit of the hose is the same of the area where the water exist the hydrant, I can assume using the equation of continuity that the velocity that the water is being pumped will the the same at the exit of the hose and I can find that value.
In this case, should I imagine the water like a solid object being launched from the ground, or is there any other equation to use when we are dealing with fluids?
 

Answers and Replies

  • #2
21,636
4,914
This is really a "projectile problem." Treat each little parcel of water exiting the hose as a separate (non-interacting) mass. You know the initial velocity of the projectile and the angle that it is launched. Determine the maximum height that the projectile reaches.
 
  • #3
6,054
391
If you know the velocity of water exiting the hose, do you really need to know anything else to find how high it can go?
 
  • #4
Thank you for you explanation Chestermiller, now I understand. I was looking at this as a pressure problem, but I just need to see water as a projectile and it's solved :)
 

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