Flow Through Parallel Connected Circular Pipes

Go by the pressure equations.

Take the lengths of the pipe (and assuming the friction coefficents on this, may be equal, may be unequal) calculate the pressure drop in each pipe - as a function of Q_i, pipe diameter_i, viscosity etc.

Then based on the pressure drop, you get the flows Q₁, Q₂ so that the pressure equations are satisfied.

Changing the diameter of the pipe now will show fom this that the flow distribution will vary.

Providing the basic guidelines. Solve your equations, and then may be post here for review.

may be using HW or DW equations.

Hello, thank you very much first of all.

when I do this, then it is something like that:

[128(Viscosity)Q1] / [D1^4] = [128(Viscosity)Q2] / [D2^4]

Now I have Q1 and Q2, and D1 and D2 in the same equation.

Lets simplfy: Q1/D1^4 = Q2/D2^4

Now, if I change D1, what happens, I can not comment on this.

If I change D1 for instance, Will Q1 change, I think yes, it will change. What about Q2? Now this is the thing.

When I change the diameter of the first pipe, I could not say what happens to the flow rates?

Nooooooooooooooo Sb.

Mr blackflutist what I understand from ur question is that you have to evalute the the shear stress distribution in both pipes.

asumption:

laminar flow.

steady state flow.

fully developed (means dp/dx is constant)

so start with Navier stokes equation (cylindrical form) U theta and Uz are zero

after applying asumptions u will reduce some terms.

part a is finish now.

part b you have to find the velocity profile for each pipe, from the velocity profile u can find shear stress for each pipe

for pressure drop u can apply bernoulli equation for each pipe.

for more clarification try this link http://cambridge.org/us/engineering/author/nellisandklein/downloads/extended/Section%205.4.2%20Fully%20Developed%20Flow%20in%20a%20Circular%20Tube.pdf

NS equation u can find it in any fluid mechanic book

regards

Hi there

Actually last night I solved the problem.

It is as follows:

I have two different diameters (of pipes). Making volumetric flow rate constant (Qtotal is constant), I am just changing one of the diameters.

Assuming we are in the laminar flow region, WHEN i change the bigger diameter (lets say I increased it), I figured out that velocity decreases more than diameter, This means REYNOLDS number is decreasing, and for BOTH pipes!!!

When I decrease the DIAMETER of the big pipe, I am seeing that BOTH velocities of the flows (first and second pipe) is increasing and it causes an increase in REYNOLDS number.

Now I can easily relate shear stresses or pressue drops (actually which is very much related) with increasing or decreasing Re.

Thank you for your help

Berkan

Ok nice

could you tell us please how can you find the shear stress without velocity profile??

show the formula please.

Actually, there are two ways to calculate shear stress, one if from pressure drop, the other one is from velocity profile.

If you want to find velocity, you should combine

viscosity * (dVelocity/dr) = r/2 (dP/dx) 1st equation.

Once you combine this, you will have velocity profile, but it is not really necessary.

Because I know that

dP/dx = 128*viscosity*Flowrate/(pi*diameter^4) 2nd equation.

So I have a relation here between pressure drop and diameter.

as can be seen, as D increases, drastic reducion in the pressure drop!(taken from White 6th edition).

So I just change D, and find how velocity changes with it (flow through two circular, different diameter pipes).

--

This is one solution, other is once you get dP/dx, you can draw the velocity profile since it is :

U=(-R^2)*dP/dx*(1/4viscosity)*[1- (r/R)^2]

So once you get pressure drop, you can get velocity, and the shear stress profile. I took the first one.

thanks for reminding me, i will check velocity profile in order to be sure.

any suggestions?

berkan

Today, I talked to my lecturer,

Part b and c is correct. However, he said you should be careful about part a).

Could anyone please tell me how should I approach to the questio a)

a)the governing differential equations for the case that in both tubes laminar flows occur.

For a pipe, it is easy, but for parallel pipes?

I have to submit it in 1 day.

I desperately need your help.

regards

I can only marginally expand on what sb wrote: work with pressure as your variable. Calculate each pipe separately - i.e. the shear force due to pressure for each radius, then calculate the shear velocity-gradient that it causes, integrate from the outside to get velocity, which leads to flow, and then integrate flow to get total flow (all good high-school stuff, especially taking care of the detail - but there are plenty of places on the web you can check the end result is right).
Finally, add the flows.
Now you have total flow versus pressure - you can manipulate that to give the required form.

P.S. I think it's a well-thought-out question, and one I haven't seen before. A useful bit of meat at each stage, and readily allows the student to demonstrate that Reynolds' number cannot be independent of shape.