(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The points a, b and c and mid way along a series of tubes arranged such:

There is a tube of 4mm for 100 cm

It splits into 3 tubes of diameter 1mm, length 20 cm

It converges into a tube of diameter 6mm, length 100 cm

The fluid flowing through the tubes is 3ml/sec and has viscosity 0.01 poise (dyne*sec*cm^-2) and a density of 1g/cm^3.

The flow is laminar and the pressure at the end of the series is 0 (or atmospheric).

Calculate the transmural pressure at the points c, b and a

2. Relevant equations

Transmural pressure = Pressure(internal) - Pressure(external)

Bernoulli's - P + (pu^2)/2 = constant

Poiseullie's - delta-P = 8QµL/(pie*R^4)

Resistance = (pie *R^4) / 8QµL

Flow = velocity * cross sectional area

Flow = (P1 - P2)(pie*r^4 / 8*viscosity*length)

3. The attempt at a solution

I thought, see as we have the end pressure, and the question starts with "calculate c". First I calculated the velocity of the 3 tube systems:

First Tube - v = Flow/area = 3/0.502 = 5.97 cm/s

Second Tube - 31.83 cm/s

Third - 2.65 cm/s

But I can't really see how that would be useful. I thought I unsure if the viscosity given, 0.01 poise, is "negligible" enough that I can use Bernoulli's. So I started with working out Pressure difference between the end of the tube, and the start of the third tube and the middle of the third tube.

3 = (P1 - P2) (pie*0.6^4 / 8*0.01*100)

so Pressure difference = 58.82 dyne*ml/cm^5 = 5.882 Pascals

Seen as pressure at the end is 0, then i reasoned the pressure at the start of the tube = 5.882 Pa.

By the same logic, the midpoint, c, will be of pressure 2.947 Pa.

So I thought the transmural (difference between the inner and outside) = 2.947 at c

However, I do not know how to translate this into working out the other tube pressures, or indeed if I should have used Bernoulli's. However I don't know:

1. If I can use Bernoulli's, as there is some degree of friction

2. How I can use it to work out pressure? Considering I would need to have a pressure value to work out the constant? Unless the constant from Bernoulli's is the same for the entire system.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Transmural Pressure in Tube System Splitting and Converging

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**