Question

The length of a pipe is 1000 m and its diameter is 200 cm. If the diameter of an equivalent pipe is 40 cm, then its length is:

• A. 4000 m
• B. 32000 m
• C. 20000 m
• D. 8000 m

Answer 1

The correct option is B 32000 m

$\text{Head loss through a pipe,}{h}_f=\frac{fl{v}^2}{2gd}=\frac{fl{Q}^2\times 16}{2g{d}^5\times {\pi }^2}$
$h_f\propto \frac{l}{d^5}$

$\text{For equivalent pipe, head loss should be same for same discharge.}$

$\frac{l}{d^5}=\text{Constant}$

$\frac{1000}{(20{)}^5}=\frac{l}{(40{)}^5}$

$l=2^5\times 1000=32000m$