Answer to Question #155140 in Civil and Environmental Engineering for lameck omenyi

Question

Design a pipe line for village considering following figure. It is

stipulated that one half of the daily supply of 150 litres per capita

per day should be delivered with in eight hours. Take C=45

a)      What must be the size of the pipe to furnish the supply,

if the head available is 12 meters?

b)     If the velocity in this pipe (friction= 0.002 is

ristricted to 1.5 m/sec, find the head loss?

Answer 1

a) According to Hazen-Williams equation

Head loss $s=\frac{10.67 Q^{1.85}} {C^{1.85}d^{4.87}}$

where $Q=$ flow rate in $m^3/s$

$S=$ head loss $m$

$d=$ diameter $m$

half of 150 litres is to be suplied for atlest 8 hours in each day.

therefore

$Q=$ 0.075 $m^3/s$

$S=$ $\frac{10.67\times 0.075^{1.85}} {45^{1.85}\times d^{4.87}}$

$d=$ $\sqrt[4.87]{\frac{10.67\times 0.075^{1.85}} {45^{1.85}\times 12^{}}}$

$d= 0.08593 m$ or $d= 86 mm$

b) Assume that the total length of the pipe used to supply water is about 120 m with the provisions:

velocity=1.5 $m/s$ and a coefficient of friction = 0.002

Darcy's formula for head loss deu to friction states the following

$h\digamma$ = $\frac{4fLv^{2}} {2gd}$

where $h\digamma$ = head loss due to friction

$f$ = coefficient of friction

$L$ = lenght of pipe $m$

$v$ = velocity of water flowing

$g$ = gravitational acceleration usually 9.81$m/s^2$

$d$ = diameter of pipe in $m$

$h\digamma$ =$\frac{4\times 0.002\times 120\times 1.5^{2}} {2\times 9.81\ 0.086} = 1.28 m$