Question

If a single pipe of length L and diameter D is to be replaced by three pipes of same material, same length and equal diameter d (d < D), to convey the same total discharge under the same head loss, then d and D are related by

• A. $D=\frac{d}{3^{1/5}}$
• B. $D=\frac{d}{2^{5/3}}$
• C. $D=\frac{d}{3^{2/3}}$
• D. $D=\frac{d}{2^{3/2}}$

Answer 1

The correct option is A $D=\frac{d}{3^{1/5}}$

$\frac{L}{D^5}=\frac{L_1}{D_1^5}+\frac{L_2}{D_2^5}+\frac{L_3}{D_3^5}$
Since $L_1=L_2=L_3=L$
and $D_1=D_2=D_3=d$
$\therefore$ $\frac{L}{D^5}=\frac{L}{d^5}+\frac{L}{d^5}+\frac{L}{d^5}$
$\Rightarrow$ $\frac{1}{D^5}=\frac{3}{d^5}$
$\Rightarrow$ $D=d/(3{)}^{1/5}$