How Much Force to Hold a Fire Hose Delivering Water at High Speed?

[aishjay]

1. A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.5 cm diameter hose delivering 470 L/min through a 0.80 cm diameter nozzle?

Homework Equations

I think we need to use the continuity eqn: A1V1 = A2V2 = Q
and the Bernoulli eqn: P + (rho)gh + 1/2 (rho)v^2 = constant

The Attempt at a Solution

Using the continuity equation, I found the velocities in the nozzle and in the hose
V1 (in nozzle) = 38.97 m/s
V2 (in hose) = 1.77 m/s

Then I used the bernoulli equation to solve for the pressure in the hose.
P1 = P2 + 1/2 (rho)[(v2)^2-(v1)^2]
with P2 = 1.0*10^5 Pa
P1 = 857830.4646 Pa

Then I said P = F/A
F = PA = 857830.4646 Pa(Area of hose)
F = 3789.8 N

But this is the wrong answer - I wonder if my logic itself is faulty?

 

[GerhardGierz]

Have you tried using the change of impulse of a small mass dm of water instead? This change of impulse should be equal to the force the brave fire fighter is using to hold the nozzle.