Question

Could you please clearly explain the following:

if a nozzle has inlet pressure P_{1 ,} Velocity V₁ and H₁ .

Is this equal to outlet Pressure P₂  Velocity V₂ and H₂ (providing that the system is adiabatic)

And, can this be written:

H₁ + KE₁ = H₂ + KE₂

_{and then}

H₁ + V₁²/2 = H₂ + V₂²/2

Answer 1

By conservation of energy, the energy per unit volume in the inlet should be equal to the energy per unit volume of the fluid in the outlet.

The energy per unit volume in the inlet is

In the above equation, the first term is the pressure energy, the second term is the kinetic energy per unit volume and the third term is the potential energy per unit volume. is the density of the fluid

Similarly, the energy per unit volume in the outlet is

Therefore, conservation of energy gives

If the pressure is equal on both sides, then

cancels on both sides and one obtains

The above equation is called the Bernoulli equation.