Bernoulli’s equation cannot be applied when the flow is:

This question was previously asked in

UPRVUNL JE ME 2016 Official Paper Shift 2

- Streamlined
- Irrotational
- Rotational
- Non viscous

Option 3 : Rotational

__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.

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

- Flow is ideal i.e inviscous.
- Flow is steady i.e. time variation is zero.
- Flow is incompressible i.e. ρ is constant.
- Flow is irrotaional i.e. ωx = ωy = ωz = 0.

Hence Bernoulli's equation is not valid for rotational flow.

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