Consider a non-viscous liquid in streamline flow through a tube AB of varying cross section as shown in Fig. Let a1 and a2 be the area of cross section, v1 and v2 be the velocity of flow of the liquid at A and B respectively.

*Equation of continuity*

*Consider a non-viscous liquid
in streamline flow through a tube AB of varying cross section as shown in Fig. Let a1 and a2 be the area of cross section, v _{1}
and v_{2} be the velocity of flow of the liquid at A and B respectively.*

*Volume of liquid entering per
second at A = a _{1}v_{1}.*

*If ρ is the density of the
liquid, then mass of liquid entering per second at A = a _{1}v_{1}ρ.*

*Similarly, mass of liquid
leaving per second at B = a _{2}v_{2}ρ*

If there is no loss of liquid in the tube and
the flow is steady, then mass of liquid entering per second at A = mass of
liquid leaving per second at B

(i.e) *a*_{1}*v*_{1}*ρ** *=* a*_{2}*v*_{2}*ρ** *or* a*_{1}*v*_{1}* *=* a*_{2}*v*_{2}* *i.e. *av* = constant

This is called as the equation of continuity.
From this equation

*v **α** _{a}*

i.e. the larger the area of cross section the smaller will be the
velocity of flow of liquid and vice-versa.

**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.

**(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}

*(iii) Potential energy*

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

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Fluid Equation of continuity |

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