Question

A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 from the horizontal.
a) determine the water gauge pressure at the house

b) how high could the water shoot if it came vertically out of a broken pipe in front of the house?

Answer 1

Answer:

a) $p=964178.7\ Pa$

b) $h=98.2853\ m$

Explanation:

Given;

• depth of the water-tank, $d=5\ m$

• length of the pipe, $l=110\ m$

• inclination of the pipe from the horizontal, $\theta =58^{\circ}$

a)

Now the effective vertical height of the water column from the free surface of the water to the bottom of the pipe at house:

$h=d+l.\sin\theta$

$h=5+110\sin58$

$h=98.2853\ m$

Now the pressure due to effective water head:

$p=\rho.g.h$

where:

$\rho=$ density of the liquid, here water

$g=$ acceleration due to gravity

$h=$ height of the liquid column

$p=1000\times9.81\times 98.2853$

$p=964178.7\ Pa$

b)

Now the height of water corresponding to this pressure will be the same as the effective water head by the law of conservation of energy.

$h=98.2853\ m$