Question

water flows through a 0.6 m diameter, 1000 m long pipe from a 30 m overhead tank to a village. Find the discharge (in liters) at the village (at ground level), assuming a Fanning friction factor f = 0.04 and ignoring minor losses due to bends etc

Answer 1

Given:

Diameter of the given pipe (D) = 0.6 m

Length (L) = 1000 m

Height of the overhead tank (H) = 30 m

Fanning friction factor (f) = 0.04

To Find:

Discharge at the village (at ground level)

Solution:

We know that,

$\bold{h_f=\frac{fLV^2}{2gD}}$, where $h_f$= friction loss of the pipe and V = flow velocity in the pipe.

Putting the given values in the above equation,

$\bold{h_f=\frac{0.04\times 1000\times V^2}{2\times 9.8\times 0.6}}$          …..(1)

∴$\bold{\Delta H= H-h_f=30-h_f}$ …(2)

Now, for flow speed,

$V=\sqrt{2gh}$

or $\bold{\Delta H = \frac{V^2}{2g}}$

$=> 30-h_f=\frac{V^2}{2g}$

$=> 30-\frac{0.04\times 1000\times V^2}{2\times 9.8\times 0.6}=\frac{V^2}{2g}$

$=>V=2.95 ms^{-1}$

∴Discharge = VA=$V\times \frac{\pi D^2}{4}$=$2.95\times \frac{\pi (0.6)^2}{4}$=$0.834\hspace{1mm} m^3/s$=834 L/s  (∵$1m^3=1000L$)

∴Discharge at the village is 834 L/s.