Question

The head loss for a laminar incompressible flow through a horizontal circular pipe is $h_1.$ Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is $h_2$. The ratio $h_2/h_1$ is

• A. 1
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is C 8

$Headloss:h_f=\frac{32\mu \overline{u}L}{\rho g{D}^2}$

$h_1=\frac{32\mu \overline{u}L}{\rho g{D}^2}$

and $h_2=\frac{32\mu \times 2\overline{u}L}{\rho (D/2{)}^2}$

$=\frac{32\mu 2\overline{u}L\times 4}{\rho g{D}^2}=\frac{8\times 32\mu \overline{u}L}{\rho g{D}^2}$

$\frac{h_2}{h_1}=\frac{8\times 32\mu \overline{u}L}{\rho g{D}^2}\times \frac{\rho g{D}^2}{32\mu \overline{u}L}=8$