Total energy of a liquid : A liquid in motion possesses pressure energy, kinetic energy and potential energy.

**Total energy of a liquid**

A liquid
in motion possesses pressure energy, kinetic energy and potential energy.

**(i) Pressure energy**

It is
the energy possessed by a liquid by virtue of its pressure.

Consider
a liquid of density ρ contained in a wide tank T having a side tube near the
bottom of the tank as shown in Fig. . A frictionless piston of cross sectional
area 'a' is fitted to the side tube. Pressure exerted by the liquid on the
piston is P = h ρ g where h is the height of liquid column above the axis of
the side tube.

If x is
the distance through which the piston is pushed inwards, then

Volume
of liquid pushed into the tank = ax

∴
Mass of the liquid pushed into the tank = ax ρ

As the
tank is wide enough and a very small amount of liquid is pushed inside the
tank, the height h and hence the pressure P may be considered as constant.

Work
done in pushing the piston through the distance x = Force on the piston ×
distance moved

(i.e) W
= Pax

This
work done is the pressure energy of the liquid of mass axρ.

∴
Pressure energy per unit mass of the liquid = Pax /axp = P/p

**(ii) Kinetic energy**

It is
the energy possessed by a liquid by virtue of its motion.

If m is
the mass of the liquid moving with a velocity v, the kinetic energy of the
liquid = ½ mv^{2}

Kinetic
energy per unit mass = 1/2mv^{2}
/ m = v^{2} / 2

*(iii) Potential energy*

It is the energy possessed by a liquid by
virtue of its height above the ground level.

If *m*
is the mass of the liquid at a height *h*
from the ground level, the potential energy of the liquid = *mgh*

Potential energy per unit mass = mgh/ m = gh

Total energy of the liquid in motion = pressure energy + kinetic
energy + potential energy.

Total energy per unit mass of the flowing liquid = P/p + v^{2}/2
+ gh

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