Which of the following equation is integrated to get Bernoulli’s equation?

Explanation:

Bernoulli's Equation:

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

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

where p/ρg = pressure head or pressure energy per unit weight, v2/2g = 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.
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.