Question

State bernoulli's theorem and derive its equation

Answer 1

According to Bernoulli's theorem, the sum of the energies possessed by a flowing ideal liquid at a point is constant provided that the liquid is incompressible and non-viseous and flow in streamline.

Potential energy + Kinetic energy + Pressure energy = Constant

P+21pv2+pgh=Constant

gh+21v2+pP=C ............(11.11)

Where C is a constant.

This relation is called Bernoulli's theorem.

Dividing eqn. (11.11) by g, we get

h+pgP+21gv2=C′ ............(11.12)

Where C is another constant.

For horizontal flow, h remains same throughout.

So,

 pgP+2gv2=Constant 

or;  P+21pv2=Constant 

P is static pressure of the liquid and 21pv2 is its dynamic and velocity pressure.

Thus, for horizontal motion, the sum of static and dynamic pressure is constant. If p1v1 and p2v2 represent pressure and velocities at two points. Then

P1+21pv12=P