Question

Derive the Bernoulli’s equation from the Euler’s equation.

Answer 1

The Euler's equation for steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure and density of a moving fluid. It is based on the Newton's Second Law of Motion. The integration of the equationgives Bernoulli's equation in the form of energy per unit weight of the following fluid.

Answer 2

Dynamic of Fluid flow Bernoulli’s equation from Euler’s equation.

$\frac{dp}{р}$ + g $d_{2}$ + vdv = 0

р = constant  ⇒ flow is incomparable

$\frac{1}{р}$ { dp + g } $d_{2}$ { vdv constant }

$\frac{P}{Фg}$ + $\frac{gz}{g}$ + $\frac{v^2}{2g}$

= $\frac{c}{рg}$

= c1

$\frac{р}{pg}$ + z + $\frac{v^2}{2g}$  = constant  

$\frac{p}{рg}$ = Pressure head

z = Potential energy

 [tex]\frac{v^2}{2g}  = Velocity head

Know More

Q.1.- Bernoulli's theorem

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Q.2.- Bernoulli's equation

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Q.3.- Applications of Bernoulli's theorem.

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