Which of the following sentences are true for Bernoulli's equation?

(1) Bernoulli's principle is applicable to ideal incompressible fluid.

(2) The gravity force and pressure forces are only considered in Bernoulli's principle.

(3) The flow of fluid is rotational for Bernoulli's principle.

(4) The heat transfer into or out of fluid should be zero to apply Bernoulli's principle.

Explanation:

Bernoulli's equation is obtained by integrating Euler's equation of motion which is given by-

Euler's Equation:

\(\frac{{dp}}{ρ } + gdz + vdv = 0\;\;\;\;\;(1)\)

In Euler's equation of motion, the forces due to gravity and pressure are taken into consideration and which is derived considering the motion of a fluid element along a stream-line.

Integrating the above eq(1):

\(\smallint \frac{{dp}}{ρ } + \smallint gdz + \smallint vdv = 0\)

\(\frac{p}{ρ } + gz + \frac{{{v^2}}}{2} = C\)

\(\frac{p}{{ρ g}} + \frac{{{v^2}}}{{2g}} + z = C\;\;\;\;(2)\)

This equation is called Bernoulli's Equation.

where \(\frac{p}{ρg}\) = pressure head or pressure energy per unit weight, \(\frac{v^2}{2g}\) = kinetic head or kinetic energy per unit weight z = potential head or potential energy by unit weight.

Following assumptions are made in the derivation of Bernoulli's equation:

1. Flow is ideal i.e inviscous.
2. Flow is steady i.e. time variation is zero.
3. Flow is incompressible i.e. ρ is constant.
4. Flow is irrotaional i.e. ωx = ωy = ωz = 0.
5. Gravity and Pressure forces are taken only hence all other external forces should be zero.
6. The energy of the system is constant hence there should be no loss of energy.