How high a building could fire hoses effectively spray from

How high a building could fire hoses effectively spray from the ground? Fire hose pressures are around 1 MPa. (It is also said that larger fire engine mounted pumps can deliver from 90-300 gallons per minute, and hoses can be as wide as 30 cm diameter What alternative estimate would that info give you?)

Solution

In the above situation, we apply the Bernoulli principle to obtain,

P1 + p*u*u/2 + pgh = P2 + p*v*v*/2 + pgH

Let us assume ther reference level for the above equation to be the same as that of the hose and also, water leaves the hose at very small velocity.

Hence, applying the above assumptions, we have:

P1 = P2 + pgH

Here, P2 will be the atmospheric pressure, and the P1 will be the pressure at the hose,

That is, H = (P1 - P2)/p*g

H = (1*10^6 - 1.01 * 10^5)/1000*9.81 = 0.899 * 10^3 / 9.81 = 91.64 metres

Further, for the extra information provided, we will have to take a non-zero initial velocity. Here the velocity at which the hose is delivering the water would be (Quantity / Area of cross section of the pipe)