In Lecture 10 - Dimensional Analysis, we investigated laminar flow in pipes and tubes, in which we arrived at the following statements: 0 ( ) = Or =2 2 =8 4 0 2 2 = (1) (2) At this point I remarked on the similarity to the Hagen Poiseuille Equation, and used that result to determine K = 16. However, this was unnecessary. We can complete the derivation of the Hagen Poiseuille result by resorting to an overall force balance on the pipe, and an invoking the definition of a Newtonian Fluid. a) Beginning with an overall force balance on the fluid in a differential section of pipe, Cross-section area of pipe = Differential area of pipe wall Shear force; obtain =2 (3) Substitute in the definition for a Newtonian fluid, integrate this with respect to x, then integrate again with respect to r to obtain a velocity profile v(r) for flow in a tube. \