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Water Hose Force Problem

  1. Apr 29, 2008 #1
    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?

    2. Relevant 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

    3. 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?
     
  2. jcsd
  3. Apr 30, 2008 #2
    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.
     
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