Firefighters arrive to the scene of a building on fire, the roof is burning at a

Question

Firefighters arrive to the scene of a building on fire, the roof is burning at a height h from the ground. At ground level, there is a pipe pointing straight up to the fire (assume there is no horizontal path for the water to travel it only needs to reach the height h vertically) that has a nozzle with radius r. You also know that the volume flow rate is Q. What is the pipe pressure needed to send the water h meters up to the fire? I thought it'd just be rho(of water)gh since bernoullis equation P1=P2 but I feel this is not right can someone please answer and explain why best you can please and thank you.

Explanation / Answer

According to bernoullis equation

P + rho*g*h + 1/2*rho*v2 = constant

Here, v = Q/A

             = Q/(pi*r2)

=> pressure needed = rho*g*h + 1/2*rho*(Q/(pi*r2))2

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