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Fluid Flow and Projectile Motion

  1. Nov 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Water travels through a pipe with a radius of 1 inch at a speed of 2 m/s. There is a nozzle at the end of the pipe with a radius of 1/4 inch. The pipe is horizontal and 2m above the ground. How far does the water travel in the air before hitting the ground?

    r1 = 1 in.
    r2 = 1/4 in.
    V1 = 2 m/s
    y = 2 m

    2. Relevant equations

    A1V1=A2V2
    A = ∏r2
    Δx = Vxt

    3. The attempt at a solution

    I found that A1 = 3.14 in.2 and A2 = .20 in.2
    I plugged those in and found V2 = 31.4 m/s2.

    Now I think I have to find t so I can work with Δx = Vxt but I'm not sure how to go about that or if that's even the direction I should be taking.

    EDIT: I tried using kinematics, re-arranging V2 = V0^2 + 2aΔx. I plugged my values in to -V0^2 / 2a = Δx and got -31.42 / 2(9.81) = 50.3 m
    Would that be correct?
     
    Last edited: Nov 21, 2013
  2. jcsd
  3. Nov 21, 2013 #2
    You did not have to. All you need is the ratio ## \frac {A_1} {A_2} = \frac { \pi r_1^2 } {\pi r_2^2 } = \left( \frac {r_1} {r_2} \right)^2 = 16 ##, so the velocity at the nozzle is 32 m/s exactly.

    The result is inaccurate, and the dimension is wrong.

    The rest of the problem is simple projectile motion. You know the initial velocity and the initial height. Find where it strikes the ground.
     
  4. Nov 21, 2013 #3
    The water is traveling both horizontally and vertically. They want you to find how far it travels horizontally when it hits the ground. How long does it take for an object dropped from a height of 2 m to reach the ground? How far does an object travel horizontally in that amount of time if its horizontal speed is 32 m/s?
     
  5. Nov 21, 2013 #4
    I got it.
    t = .64 s
    displacement = 32(.64) = 20.4 m

    Thanks guys!
     
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