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Fluid dynamics problem -- Tanks Connected by Capillary

  1. Sep 28, 2014 #1
    1. The problem statement, all variables and given/known data
    Two tanks are connected via a capillary pipe, with one tank over the other. The speed in which the liquid flows from the upper tank to the lower tank is 3472 cm/min. The height of the liquid inside the upper tank is 30cm from the bottom of the tank. The capillary pipe sticks 3cm down into the liquid of the lower tank, and the length of pipe between the two tanks is 35cm. (total pipe length 35+3=38cm) The density of the liquid is 1000 kg/m3, and the viscosity is 1cP.

    Find the diameter of the capillary pipe. (Hint: Assume laminar flow in the pipe, f=16/Re, but check that this assumption is correct)

    2. Relevant equations
    Not quite sure.

    3. The attempt at a solution
    I assumed that it was as simple as putting in Bernoulli equation, but I cant seem to solve it that way, and I dont see how I can involve the diameter of the pipe as an unknown... Looking for a push in the right direction here.
     
  2. jcsd
  3. Sep 28, 2014 #2
    Have you learned yet about pressure drop in flow through a pipe? Have you learned about laminar flow? Have you learned about friction factors and Reynolds numbers?

    Chet
     
  4. Sep 28, 2014 #3
    A bit, yes. I thought about using Bernoulli's equation, and solving for hf (friction loss) and then using 4f(L/D)*(v^2/2g)=hf to solve, as that brings D into the equation, but the problem then becomes that I am not entirely sure if the height differences in Bernoulli's should be 35cm, or 38. (top of the liquid, or bottom of the pipe) I was thinking top of the liquid, since then p1=p2, and v1=v2, so bernoulli's equation simplifies quite a bit, but when I try to solve it that way, I dont get any of the 5 possible answers. (it has a multiple choice answer)
     
  5. Sep 28, 2014 #4

    SteamKing

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    The clue here is the OP mentions 'capillary pipe' and then tells you that the friction factor f = 16/Re, because of laminar flow in the pipe.
    What you have here is fluid flow with friction, which is not covered just by the Bernoulli equation.
     
  6. Sep 28, 2014 #5
    The form of Bernoulli's equation that I am using is:

    p1/ρg + Z1 +v12/2g = p2/ρg + Z2 +v22/2g + hf

    Where:
    p1= The pressure at point one
    p2= The pressure at point two
    Z1= The height at point one
    Z2= The height at point two
    ρ= The density of the liquid
    hf= The pressure lost due to friction

    The equation I have been using for hf is:

    hf=4f*L/D*v2/2g

    Where:
    L= The length of the pipe
    D= The diameter of the pipe
    v= The velocity of the liquid in the pipe

    I have used the equation for Reynolds number, which is:
    Re=(ρ*v*D)/μ

    Where:
    μ= The viscosity of the liquid
    Re= Reynolds number

    When I replace the f in the hf equation with 16/Re, and then replace that Re with the Reynolds number equation, it leaves me with just the D as an unknown, since I have information on hand to find everything else. The issue is that when I solve for it, I dont get the right answer.

    So I am curious if I am going about this in the correct manner or not.
     
  7. Sep 28, 2014 #6

    SteamKing

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    Well, we haven't seen any of your actual calculations yet. There may be a problem with units, arithmetic errors, ...
     
  8. Sep 28, 2014 #7
    Something they forgot to mention in the problem statement is that the lower tank is open to the atmosphere, so that the capillary tube dips down 3 cm below the surface of the water. So, if d1 is the depth of water in tank 1, and d2 is the depth that the capillary tube dips into the water in the lower tank, what are the pressures p1 and p2 at the entrance to the capillary and at the exit of the capillary, respectively (in terms of rho, g, and d1 or d2)? This is probably where you are running into trouble.
     
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