Fluid dynamics problem -- Tanks Connected by Capillary

[Latsabb]

Homework Statement

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)

Homework Equations

Not quite sure.

The Attempt at a Solution

I assumed that it was as simple as putting in Bernoulli equation, but I can't seem to solve it that way, and I don't see how I can involve the diameter of the pipe as an unknown... Looking for a push in the right direction here.

 

[Chestermiller]

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

 

[Latsabb]

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 don't get any of the 5 possible answers. (it has a multiple choice answer)

 

[SteamKing]

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.

 

[Latsabb]

The form of Bernoulli's equation that I am using is:

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

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
h_f= The pressure lost due to friction

The equation I have been using for h_f is:

h_f=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 h_f 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 don't get the right answer.

So I am curious if I am going about this in the correct manner or not.

 

[SteamKing]

Well, we haven't seen any of your actual calculations yet. There may be a problem with units, arithmetic errors, ...

 

[Chestermiller]

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.