Question

Water is flowing through a horizontal tube 4km in 4cm in radius at a rate of 20 litres. Calculate the pressure required to maintain the flow in terms of the height of mercury column?

Answer 1

Hint: Water flow is determined by the water pressure gradient.
The flow of water or any other fluid is directly proportional to the pressure difference.
Higher the pressure, greater the flow rate.

Complete step by step answer:
\[20{\text{ }}litre = {\text{ }}0.02{m^3}\]20 litre= 0.02m3
$\implies$ \[Area{\text{ }}of{\text{ }}tube{\text{ }} = {\text{ }}\pi {\text{ }}{R^2} = 3.14{\text{ }}*{\left( {0.04} \right)^2} = {\text{ }}0.005024{\text{ }}{m^2}\]Area of tube = π R_2 =3.14 *(0.04)2 = 0.005024 m^2
Velocity Of Water = $volume/area = 0.02/0.005024 = 3.98m/s \\$
Velocity Pressure = $(\rho {V^2})/2 \\$
$\rho$ (density of water) = $1000kg/m_3 \\$
Velocity Pressure = $(1000*3.98*3.98)/2 = 7920Pa \\$
$\implies 1 atm = 101,300 Pa(760 mm of Hg) = (7920/101,300)*760 = 60mmHg \\
$

Note:
Remember that according to Bernoulli’s principle, if the speed of fluid increases, the pressure of the fluid decreases and vice versa.
But there are certain limitations in Bernoulli’s principle.
It is not applicable for turbulent or non-steady flow of fluids.
The liquid flow can be affected by the external force of a liquid.