Question

In steady laminar flow of a liquid through a circular pipe of internal diameter D, carrying a constant discharge, the hydraulic gradient is inversely proportional to

• A. $D$
• B. $D^2$
• C. $D^4$
• D. $D^5$

Answer 1

The correct option is C $D^4$

For Laminar flow through pipe.

Hagen-Poiseuilie's eq.

$\frac{P_1-P_2}{\rho g}=\frac{32\mu \overline{v}L}{\rho g{D}^2}Q=\left[\frac{\pi }{4}{D}^2\right].\overline{u}$

$\text{or}\frac{P_1-P_2}{\rho g}=\frac{128}{\pi }\frac{\mu QL}{\rho g{D}^4}$