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Bernoulli's Equation is obtained by
1. Integration of Euler's Equation
2. Differentiation of Euler's Equation
3. Double differentiation of Euler's Equation
4. Newton's law of motion

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Correct Answer - Option 1 : Integration of Euler's Equation

Explanation:

Bernoulli's equation: it is known as conservation of energy and is obtained by integrating the Euler's equation of motion.

\(\int {\frac{{\rm{P}}}{{\rm{\rho }}}} {\rm{ + }}\int {{\rm{gdz + }}\int {{\rm{VdV = const}}} } \)

The Assumptions of Bernoulli equation are:

  1. Steady flow that is the flow condition do not change with time at any point.
  2. Incompressible flow, ρ is constant.
  3. Non viscous, ideal flow.
  4. Energy is niether added nor removed from system.


In terms of energy per unit mass Bernoulli equation is:

\(\frac{P}{\rho}+gz+\frac{V^2}{2}=const\)

In terms of energy per unit weight Bernoulli equation is:

\(\frac{P}{\rho g}+z+\frac{V^2}{2g}=const\)

where,

P/γ = P/ρg = Pressure energy per unit weight of fluid or pressure head

v2/2g = Kinetic energy per unit weight or kinetic head

z = Potential energy per unit weight or potential head

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