Exercise 12 Solution

Substituting 64/Re and the equation for the Reynolds number into Equation 4 proves that this results in the Hagen-Poiseuille equation for a circular pipe.

Reynolds Number: \displaystyle Re=\frac{VD\rho }{\mu }=\frac{VD}{\nu }

Equation 4: \displaystyle \frac{\Delta p}{L}=f_{D}\frac{\rho }{2}\frac{V^{2}}{D}

Hint: Remember that the radius of a circle is one half the diameter.

\displaystyle \frac{\Delta p}{L}=\frac{64\mu }{VD\rho }\frac{\rho V^{2}}{2D}

\displaystyle \frac{\cancel{64}\mu }{\cancel{V}D\rho }\frac{\rho V^{\cancel{2}}}{\cancel{2}D}=\frac{32\mu V}{D^{2}}

\displaystyle \frac{32\mu V}{D^{2}}=\frac{32\mu V}{2^{2}r^{2}}

\displaystyle \frac{\cancel{32}\mu V}{\cancel{2}^{\cancel{2}}r^{2}}=\frac{8\mu V}{r^{2}}

Return to Exercise 12

Return to where text linked to Exercise 12


Introduction to Karst Aquifers Copyright © 2022 by Eve L. Kuniansky, Charles J. Taylor, and Frederick Paillet. All Rights Reserved.