Each term in Bernoulli's equation represents:

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 eq(1):
• \(\smallint \frac{{dp}}{ρ } + \smallint gdz + \smallint vdv = 0\)
• \(\frac{p}{ρ } + gz + \frac{{{v^2}}}{2} = C\)
• \(\frac{p}{{ρ g}} + \frac{{{v^2}}}{{2g}} + z = C\;\;\;\;(2)\)
• 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.
• Hence from the above equation, we can see that Bernoulli's equation represents energy per unit mass

Additional Information

Following assumptions a re 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.