Question

An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters $d_1$ and $d_2$ (where $d_1$ = $4d_2$) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is

• A. 2

Answer 1

The correct option is A 2

$d_1=4d_2$

$\frac{fl{v}_1^2}{2g{d}_1}=\frac{fl{v}_2^2}{2g{d}_2}$

$\Rightarrow \frac{V_1^2}{d_1}=\frac{V_2^2}{d_2}$

$\frac{V_1^2}{V_2^2}=\frac{d_1}{d_2}=4$

$\frac{V_1}{V_2}=2$