Question

derivation of Bernoulli's theorem ​

Answer 1

Answer:

I will you the simplest method to derive Bernoulli's theorem.

Consider the following types of energies available when a fluid is flowing through a pipe.

1. Kinetic energy per unit volume

= [(1/2)*m*v^2 ]/ Volume

= (1/2)*p*v^2,

where p = density of the fluid, m = mass,

v = velocity of fluid.

2. Potential energy per unit volume.

= (m*g*h)/volume

= p*g*h , where p= density, g = gravity and h = height from reference frame.

3. Thermodynamic work per unit volume

=( P* volume)/ volume

= P , where P is the pressure in the fluid column.

NOW, FOR ANY NON VISCOUS, NON COMPRESSIBLE FLUID (NEWTONIAN FLUID) , the sum of the above energies remain constant.

Therefore,

[ P + {(1/2) *p*v^2} + {p*g*h} = constant ]

This is the easiest proof of Bernoulli's theorem.