Question

According to Bernoulli's equation \[\dfrac{P}{{\rho g}}({\text{A}}) + h{\text{(B)}} + \dfrac{1}{2}\dfrac{{{v^2}}}{g}{\text{(C)}} = {\text{constant}}\].The terms A, B and C generally called respectively.
(A) Gravitational head, pressure head and velocity head.
(B) Gravity, Gravitational head and velocity head.
(C) Pressure head, gravitational head and velocity head.
(D) Gravity, pressure and velocity head.

Answer 1

Hint:In an incompressible, ideal fluid when the flow is steady and continuous, the sum of pressure energy, kinetic energy and potential energy will be constant along a streamline
\[\dfrac{P}{{\rho g}} + h + \dfrac{1}{2}\dfrac{{{v^2}}}{g} = {\text{constant}}\]
Here, \[P\]is the pressure, \[\rho \]is density, \[g\]is the acceleration due to gravity, \[h\] is the height and \[v\] is the velocity of fluid

Formula used:
The expression for the Euler equation of motion is written as,
\[\dfrac{{dp}}{\rho } + vdV + gd(h) = 0\]
Here, \[\dfrac{{dp}}{\rho }\] is pressure term, \[vdV\] is velocity term and \[d(h)\] is the gravitational term.
The expression for the Bernoulli equation is written as,
\[\dfrac{P}{{\rho g}} + h + \dfrac{1}{2}\dfrac{{{v^2}}}{g} = {\text{constant}}\]
Here, \[P\]is the pressure, \[\rho \]is density, \[g\]is the acceleration due to gravity, \[h\] is the height and \[v\] is the velocity of fluid

Complete step by step answer:
Write down the expression for the Euler equation of motion
\[\dfrac{{dp}}{\rho } + vdV + gd(h) = 0\]
Here, \[\dfrac{{dp}}{\rho }\] is pressure term, \[vdV\] is velocity term and \[d(h)\] is the gravitational term.
Integrate the above equation,
\[
\int {\dfrac{{dp}}{\rho }} + \int {vdV} + g\int {d(h)} = 0 \\
\therefore\dfrac{P}{{\rho g}} + h + \dfrac{1}{2}\dfrac{{{v^2}}}{g} = {\text{constant}} \\
\]
Therefore the term\[\dfrac{P}{{\rho g}}\], \[h\] and \[\dfrac{1}{2}\dfrac{{{v^2}}}{g}\] are called Pressure head, Gravitational head and velocity head respectively.
Hence,the option C is the correct choice.

Note:Term which has pressure term involved is known as Pressure head, term which has the height term involved is known as the gravitational head and the term which involves the velocity term known as velocity head. Therefore, option C is the correct representation.