Question

The pressure energy per unit mass of liquid of density $\rho$ at a pressure $P$ is
A. ${\displaystyle \frac{P}{\rho }}$
B. $\rho \times P$
C. ${\displaystyle \frac{\rho }{P}}$
D. $$\sqrt{{\displaystyle \frac{P}{\rho }}}$$

Answer 1

Hint:Pressure energy of a liquid is nothing but the energy that is stored in each unit of the liquid. The units and dimensions of this quantity is the same as that of energy. This quantity is highly useful in order to determine the behavioural characteristics of liquids.

Complete answer:
We can say that the pressure energy of a liquid is the same as that of the energy that is contained inside the liquid. The pressure energy can be deduced as the product of pressure and volume, that is $PV$. We can find the value of the pressure energy per unit mass by dividing it was the quantity of mass that is $m$.

Hence, pressure energy per unit mass can be written as ${\displaystyle \frac{PV}{m}}={\displaystyle \frac{P}{\rho }}$
We have expressed ${\displaystyle \frac{V}{m}}$ as $${\displaystyle \frac{1}{\rho }}$$ which is nothing but the reciprocal of density. We have derived this from the known fact that density is the quotient of the mass and the volume of the liquid.

Thus we can arrive at a conclusion that option A is the correct answer.

Note:We find the application of pressure energy in the Bernoulli’s theorem where the pressure energy per unit volume gives us the value of the hydrostatic pressure of the fluid. Sometimes the question can be framed in this manner as well. Hence, the student must be aware of the connection between the pressure energy and Bernoulli's principle.