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Fluid Dynamics

  1. Mar 14, 2014 #1
    1. The problem statement, all variables and given/known data
    The water from a pipe flows into a tank of volume 180 m^3. If the tank is initially empty, how long will it take to fill the tank?

    I know that water is coming out of the pipe with a velocity of 22 m/s, and the diameter of this end of the pipe is 48 cm.


    2. Relevant equations
    This is what I don't know.
    Is it v1A1=v2A2? or p1+1/2ρv1^2+ρgy1=p2+1/2ρv2^2+ρgy2?


    3. The attempt at a solution
    v1A1=v2A2

    22 m/s*.10898 (A1)=0?
     
  2. jcsd
  3. Mar 14, 2014 #2
    You're kind of using the formula wrong. I might suggest calculating it with all the units explicitly stated and then look at the question again.
     
  4. Mar 14, 2014 #3
    If you know the cross sectional area of the pipe and the average velocity of the water coming out of the pipe, to you know the formula for calculating the volumetric throughput rate coming out of the pipe?
     
  5. Mar 14, 2014 #4

    Simon Bridge

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    Or - don't worry about the equation: just look at the geometry.
    What is the volume of water flowing through the pipe each second?

    You know how to find the volume of a cylinder right?
     
  6. Mar 14, 2014 #5
    Okay so my units on each side will be meters^3/sec. I don't understand how to just get m^3 without taking out the velocity (which I am going to need to use right?)
     
  7. Mar 14, 2014 #6
    The only formula I can find that I feel applies is V1A1=V2A2.
    Is this not the correct equation to use?
    Even if it is, my confusion is what goes on the right side of the equation? Being that V2 and A2 don't really apply to the information I am given.
     
  8. Mar 14, 2014 #7
    V=∏r^2h
    ∏(.325m)^2(.65m)=.2157m^3
    How does this tell me the flow rate per second?
     
  9. Mar 14, 2014 #8
    I'm sure your text or course notes talked about the formula for volumetric flow (you actually already stated it in context)?

    Suppose you were standing next to the 48cm dia. pipe and you measured an h=1m length of pipe. You could wait for t=1 second and measure the volume of water V flowing by in that time and this would give you Q=V/t (the volumetric flow rate).

    But V = Ah (volume)
    and v = h/t (speed)
    therefore Q = vA

    Hopefully you can take it from there.
     
  10. Mar 14, 2014 #9

    Simon Bridge

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    Since you are told that the flow rate is constant, the volume of water through the pipe in one second is the flow rate.

    Don't worry about these terms right now. I am trying to get you off your dependence on memorizing equations.

    ... that's the volume of a cylinder radius r and length h - good.
    (It's better if you use "π" instead of "∏" there, but I can see what you mean.)

    You used r=0.325m and h=0.65m ... why? Where do these figures come from?

    If the numbers you use have no relation to the problem then it won't of course.

    The pipe is cylindrical with diameter d=0.48m
    The water flows in the pipe at speed v=22m/s

    The water leaving the pipe is basically a cylinder that grows in length... or it would be if it didn't fall etc. So imagine water pouring out the pipe in a long straight cylinder of water. You can work out the volume of the water leaving the pipe by working out the volume of the "cylinder" of water.

    I'm asking you to use these figures, and the equation for the volume of a cylinder, to work out the volume of water that left the pipe in 1 sec.

    If you know the volume of water that flows out the pipe in 1 second, then you can work out howm many seconds are needed to fill the tank.
     
  11. May 21, 2015 #10
    solution:
    rate of flow can be determined by,
    wkt v=22m/s area of hole:3.14*(0.24)*(0.24)
    rate of flow =22*3.14*(0.24)*(0.24)m^3/s
    time taken : 180m^3/(22*3.14*(0.24)*(0.24))m^3/s
     
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