Bernoulli Equation is derived from _______. 

Explanation:

Bernoulli's equation is obtained by integrating Euler's equation of motion involves the assumption that velocity potential exists and that the flow condition do not change with time at any point. :

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

If the flow is incompressible, ρ is constant and

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

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

Bernoulli’s Equation is known as the conservation of energy principle and states that in a steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consists of pressure energy, kinetic energy and potential energy or datum energy.

\(\frac{P_1}{\rho_1 g}+\frac{V_1^2}{2g}+Z_1=\frac{P_2}{\rho_2 g}+\frac{V_2^2}{2g}+Z_2\)

All the terms of Bernoulli’s equation:

\(\frac{P}{\gamma } + \frac{{{v^2}}}{{2g}} + z = C\)

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