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.