Question

The pressure energy per unit volume of a liquid is:
$\begin{array}{rl}& A){\displaystyle \frac{P}{\rho }}\\ & B)P\\ & C)P\times \rho \\ & D){\displaystyle \frac{\rho }{P}}\end{array}$

Answer 1

Hint: Pressure energy of a liquid is the energy that is stored in each unit of the liquid. It has the same units and dimensions as that of energy. So, the quantity obtained by taking pressure per unit volume must be the same as that obtained by dividing energy per unit of volume. The quantities pressure and pressure energy are more useful in describing the behavior of liquids instead of quantities like forces.
Formula Used:
$\text{Pressure Energy=}{\displaystyle \frac{Energy/Work}{Volume}}$

Complete answer:
Pressure Energy a liquid is the same as energy contained in a liquid.
$\begin{array}{rl}& {\displaystyle \frac{{}^{Energy}/{}_{Work}}{Volume}}\\ & ={\displaystyle \frac{F\times d}{A\times d}}\\ & ={\displaystyle \frac{F}{A}}\\ & =P\end{array}$
Here,
F is the force exerted on the liquid.
A is the area of the liquid on which force or pressure is exerted.
d represents the distance.
P represents Pressure.
The pressure energy per unit volume of a liquid is given by the Pressure (P).

Thus, the correct option is (B)Pressure

Additional Information:
The term Pressure Energy arises in Bernoullis’s equation, where the Pressure energy per unit volume gives the measure of hydrostatic pressure of the fluid. Pressure energy is the energy contained in each unit of the liquid due to the effect of thermal energy of the atoms and molecules. The S.I unit of Pressure is Pascal which can be expressed as Newton per square meters.

Note:
The pressure energy per unit volume of a liquid can alternatively be obtained by another method. Considering pressure energy as pressure times the volume of the liquid, we can proceed as follows:
$\begin{array}{rl}& {\displaystyle \frac{\text{Pressure Energy}}{Volume}}\\ & ={\displaystyle \frac{P\times V}{V}}\\ & =P\end{array}$
The important point to remember is how to express pressure energy .It can be expressed in terms of energy or pressure times the volume of the liquid.