Correct Answer - Option 3 : Steady, incompressible and irrotational
Concept:
Bernoulli’s equation:
Bernoulli’s equation between any two points in the form of energy per unit weight is given by,
\(\frac{P}{\gamma} + \frac{v^2}{2g}\) + z = constant
The following are the
assumptions made in the derivation of Bernoulli’s equation:
- The fluid is ideal, i.e Viscosity is zero or inviscid
- The flow is steady
- The flow is incompressible
- The flow is irrotational
-
Bernoulli's equation can be obtained by integrating Euler's equation as follows -
We know Euler's equation,
\(\frac{dP}{\rho}\) + vdv + gdz = 0
On intergrating, along a stream line between two points
\(\int\limits _1^2\)\(\frac{dP}{\rho}\) + \(\int\limits _1^2\)vdv + \(\int\limits _1^2\)gdz = 0
\(\frac{P_1}{\rho} + \frac{v_1^2}{2} + gz_1 = \frac{P_2}{\rho} + \frac{v_2^2}{2} + gz_2\)
⇒ \(\frac{P}{\gamma} + \frac{v^2}{2g}\) + z = constant
Here,
\(\frac{P}{\gamma}\) - static head (m)
\(\frac{v^2}{2g}\) - Dynamics head (m)
z - datum head (m)
P - Pressure (Pa)
v - Average velocity (m/sec)
