Statement (I): Bernoulli’s equation is applicable to any point in
Statement (I): Bernoulli’s equation is applicable to any point in the flow field provided the flow is steady and irrotational
Statement (II): The integration of Euler’s equation of motion to derive Bernoulli’s equation involves the assumption that velocity potential exists and that the flow condition do not change with time at any point.
A. Both Statement (I) and Statement (II) are individually true; and Statement (II) is the correct explanation of Statement(I)
B. Both Statement (I) and Statement (II) are individually true; but Statement (II) is NOT the correct explanation of Statement (I
C. Statement (I) is true; but Statement (II) is false
D. Statement (I) is false; but Statement (II) is true
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Bernoulli's equation is obtained by integrating the 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
