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Incompreshible flow question

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Water (of density 1000 kg/m^3) flows into a cylindrical tank through two pipes at mass flow rates of 6 kg/sec and 10 kg/sec respectively, and leaves the tank via a circular outlet pipe of 20 cm diameter. If the water level in the tank is to remain constant, calculate the average flow velocity in the outlet pipe.


    2. Relevant equations

    Q1 + Q2 = Q3 ---> A1*u1 + A2*u2 = A3*u3

    3. The attempt at a solution

    I'm really tempted to just say, well the water coming in is 10 kg/sec and 6 kg/sec so the water exiting must be 16 kg/sec. I'm not sure you can do that though, but there are too many unknowns! You have A3, but not A1 or A2. You have u1 and u2, but not u3 (what you're solving for).

    A1(6 kg/sec) + A2 (10 kg/sec) = pi*0.2m^2*u3

    Can anyone steer me in the right direction?
     
  2. jcsd
  3. Jan 18, 2012 #2
    You are correct, the mass flow rate coming in equals mass flow rate going out via continuity of mass equations. Remember mass flow rate = density*area*velocity. You know the mass flow rate out, area and density. Bingo!
     
  4. Jan 18, 2012 #3
    Are you saying the mass flow rate out has to be equal to 16 kg/sec?
     
  5. Jan 18, 2012 #4
    Yes, if the level of the water is not going up the mass of water going in must equal the mass of water going out so 16 kg/s is leaving the outlet pipe.
     
  6. Jan 18, 2012 #5
    right. So I have 16 kg/s in the outlet pipe, but how do I find the velocity from that?
     
  7. Jan 18, 2012 #6
    I got an answer, but it seems rather low. I think I saw somewhere that Velocity = flowrate/area*density

    so I have 16/(pi*0.04 m^2)*(1000)
    The units work out to be m/s and I got 0.127 m/s That's some slow moving water! Does this work?
     
  8. Jan 18, 2012 #7
    I think you have got the diameter and area of the outlet mixed up... it is 0.2m diameter so the area is π x 0.1^2
     
  9. Jan 18, 2012 #8
    Thanks. You're right. That changes the answer to 0.509 m/s
    Still seems a little low though.
     
  10. Jan 18, 2012 #9
    mmmmm. I think it is OK 20cm is a large pipe:biggrin:
     
  11. Jan 18, 2012 #10
    That looks like the correct answer
     
  12. Jan 18, 2012 #11
    Thanks for the help. I'll run with it.
     
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