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.

 

[Moetasim]

Your calculations and approach seem correct, but there may be some errors in your calculations or assumptions. It would be helpful to double check your units and make sure they are consistent throughout the calculation. Additionally, make sure you are using the correct values for density and gravity in the Bernoulli equation. It may also be helpful to look at the problem from a different perspective, such as using the force equation F = ma to find the force required to accelerate the water from the hose to the nozzle.