Question

pressure head in Bernoulli’s equation is
A) $\dfrac{{P\rho }}{g}$
B) $\dfrac{P}{{\rho g}}$
C) $\rho g$
D) $P\rho g$

Answer 1

Hint: Pressure head is the height of a column of liquid which corresponds to the pressure in a liquid.

Complete step by step answer:
According to Bernoulli’s theorem
$\dfrac{P}{\rho } + \dfrac{{{v^2}}}{2} + gz = C$
Where,
$p = $pressure of the liquid
$\rho = $density of liquid
$z = $elevation
$g = $acceleration due to gravity

If we divide Bernoulli's equation by $g$, we obtain a head of pressure, kinetic and elevation.
The equation will become as follows:
$\dfrac{P}{{\rho g}} + \dfrac{{{v^2}}}{{2g}} + z = C$

Now each term has the dimension of energy per unit mass of fluid.
The equation states that the energy at any point in the flowing fluid is equal to the sum of the pressure head, kinetic head and elevation head.

So the pressure term in the equation is called pressure head
Pressure head $ = \dfrac{p}{{\rho g}}$
It represents the flow of energy of a column of liquid whose weight is equal to the pressure of the liquid.

B) is correct

Additional information:
The kinetic head and elevation head are explained as follows
- Kinetic head: The kinetic head represents the kinetic energy of the liquid. It is the height in feet that a flowing liquid would rise in the column if all of its kinetic energy is converted into potential energy. It is also known as velocity head.
- Elevation head: The head represents the potential energy of the fluid due to its elevation above the reference level. It is also known as gravitational head.

Note: The term ‘head’ is a simple way of expressing the difference in height in any quantity. Pressure head should not be confused by pressure difference.