Solving Poiseuille's Law Flow Rate Problem | Help Needed

[rddimtbo]

I'm having difficulty with a question and would appreciate a point in the right direction. The question is, "What is the flow rate of a tube that consists of two sections, the first with length 20cm and radius 0.15cm and the second part with length 1.0 cm and .05cm radius. The pressure difference across the entire length is 3 cmHg and viscosity is .801 cp.
We were given a hint that we should refer to gauge pressure (ie: P1 = 3 cm Hg and P3 = 0) with this one, and I'm still not getting the correct answer (which is 9.83 cm^3/s) Any ideas as to which direction to turn would?

My work:
For section 1:
V/t = 3.14 * r1^4 (p1-p2)/8(eta)L1
For section 2:
V/t = 3.14 * r2^4 (p2-p3)/8(eta)L2
and
p1-p3 = 3 cm Hg
When I calculate this as p1 equalling 3 cm Hg and p1 equalling 0 cm Hg, I am able to find p2 and then apply this to the first equation to solve for V/t. My answer is not anywhere close to the actual. Is there another equation i should be considering in this problem? If there is, I don't see it.

 

[AvroArrow]

Any help is much appreciated. You should note that the pressure difference across the two sections is not the same. The pressure at the end of the first section (P2) is not 0 cmHg, and the pressure at the start of the second section (P2) is not 3 cmHg. You can calculate the pressure difference across each section separately by solving each of the equations you wrote. Once you have the pressure difference across each section, you can solve for the flow rate through each section and then sum them together to get the total flow rate.

 

[M98Ranger]

It looks like you are on the right track with using Poiseuille's Law to solve this problem. However, there may be a few things that you are missing in your calculations.

Firstly, make sure that you are using the correct units for all of your variables. In this case, the pressure difference should be in units of Pascals (Pa) rather than cmHg. You can convert cmHg to Pa by multiplying by 133.3.

Secondly, you should also take into account the fact that the flow rate is the same for both sections of the tube. This means that the volume flow rate in section 1 should be equal to the volume flow rate in section 2. This can be represented as:

V1/t = V2/t

You can use this equation to solve for one unknown variable in terms of the other.

Lastly, make sure that you are using the correct values for the viscosity (eta) and the lengths of the two sections of the tube. Double check your calculations to ensure that all of your values are correct.

If you are still having trouble, you may want to reach out to your instructor or classmates for further clarification. They may be able to provide additional guidance or point out any mistakes in your calculations.

I hope this helps and good luck with your problem!