The pressure drop per unit length, , for the flow of blood

Chapter 7, Problem 7.35

(choose chapter or problem)

The pressure drop per unit length, \(\Delta p_\ell\), for the flow of blood through a horizontal small-diameter tube is a function of the volume rate of flow, Q, the diameter, D, and the blood viscosity, \(\mu\). For a series of tests in which D = 2 mm and \(\mu=0.004 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\), the following data were obtained, where the \(\Delta p\) listed was measured over the length, \(\ell= 300\) mm.

               

Perform a dimensional analysis for this problem, and make use of the data given to determine a general relationship between \(\Delta p_\ell\) and Q (one that is valid for other values of \(D, \ell\), and \(\mu\)).