Question

Water is pumped at a steady uniform flow rate of 0.01 m${}^3$/s through a horizontal smooth circular pipe of 100 mm diameter. Given that the Reynolds number is 800 and g is 9.81 m/s${}^2$, the head loss (in meters, up to one decimal place) per km length due to friction would be

• A. 66.11

Answer 1

The correct option is A 66.11

Head loss due to frictions,

$h_L=\frac{fL{Q}^2}{12.1d^5}$

Here,

$f=frictionfactor$

$=\frac{64}{Re}=\frac{64}{800}=0.08$

$\therefore$ Head loss per metre length

$\frac{h_L}{L}=\frac{f{Q}^2}{12.1d^5}=\frac{0.08\times (0.01{)}^2}{12.1\times (0.1{)}^5}$

$\frac{h_L}{L}=\frac{0.8}{12.1}=0.06611metre/metre$

= 66.11 metre/km