Principle of Conservation of Energy [Fluid Flow]

PRINCIPLE OF CONSERVATION OF ENERGY

Energy can be neither created nor destroyed but it can be converted from one form to another form. This is called principle of conservation of energy. This is the basis for Bernoulli's theorem. According to this, total energy at any point remains constant. There are three different forms of energy

1. Potential energy:

The energy possessed by a fluid by virtue of its position above or below the datum line is called potential energy.

Potential energy = Wh = mgh = mgZ

Where

h = Z = height of fluid particle above datum line in m

m = mass of fluid in kg

w = weight of fluid in N

g = acceleration due to gravity

Epotential in J/kg

2. Pressure energy:

The energy due to fluids pressure is called pressure energy.

Pressure energy = PUs 

p-pressure in N/m2

Us - specific volume of fluid in m3/kg

Us = 1/ρ

so pressure energy (E)pressure = P/ ρ in J/kg

3. Kinetic energy:

The energy of the fluid by virtue of its velocity is called kinetic energy.

Kinetic energy = 1⁄2 mV2

m = mass of the fluid in kg

V = velocity of the fluid in m/s

Ekinematics in J/kg

According to the principle of conservation of energy, total energy of fluid remains constant.

Total energy = Potential energy + kinetic energy + pressure energy 

= gZ + V2/2 + P/p

Divide the above equation by g on both sides

Total head or total energy = Z + V2/2g + P/ρg

= Z + V2/2g + P/w

Since total energy or head of fluid remains constant.

Z1 + V12/2g + P1/w = Z2 + V22/2g + P2/w

This is known as Bernoulli's equation.