Blood Fluid Mechanics Homework (V. 2.0)

PE-674, Winter '99-'00, Dr. C. S. Tritt

Due 12/6

1. Show that the general Mechanical Energy Balance Equation:

Can be reduced to the Hagan-Poiseuille equation:

in the case of fully developed, laminar flow of a Newtonian fluid.

2. Use the general Mechanical Energy Balance Equation to estimate the steady‑state rate of blood infusion (in ml/min) from a 500 ml bag hung 1.00 m above a patient. Assume the blood behaves as a Newtonian fluid with a viscosity of 3.0 cp (3.0310^‑3 Pa·s). Assume the line connecting the bag to the needle has a 4.00 mm inside diameter (I.D.) and is 1.40 m long. Assume the needle has a 1.00 mm I.D. and is 60 mm long. Neglect the velocity of the blood at the inlet of the tube. Neglect losses at the connection between the tubing and the needle. I suggest you use a spreadsheet to perform the calculations for this problem and possibly use a trial-and-error approach.