Question

In the streamlined flow of a liquid, the power due to the pressure difference between the ends of the tube is

• A. Equal to a product of pressure and volume of liquid flowing per second.
• B. Equal to a product of pressure and mass of liquid flowing per second.
• C. Equal to the product of radius and coefficient of viscosity.
• D. Equal to the product of pressure and velocity.

Answer 1

The correct option is A

Equal to a product of pressure and volume of liquid flowing per second.

1. Power is defined as the rate of doing work per unit time.
2. The mathematical expression for power is $\mathrm{Power}=\frac{\mathrm{W}}{\mathrm{t}}$.
3. Streamline flow in fluids is defined as the flow in which the fluids flow in parallel layers such that there is no disruption or intermixing of the layers and at a given point, the velocity of each fluid particle passing by remains constant with time.
4. In the streamlined flow of the liquid, the product of pressure and volume of the liquid is equal to the work by liquid.
5. So work done by the liquid is $\mathrm{W}=\mathrm{P}\times \mathrm{V}$, where $\mathrm{W}$ is the work, $\mathrm{P}$ is the pressure and $\mathrm{V}$ is the volume.
6. The power in the streamlined flow of liquid is, $\mathrm{Power}=\frac{\mathrm{W}}{\mathrm{t}}=\frac{\mathrm{P}\times \mathrm{V}}{\mathrm{t}}$.

Hence, option (A) is correct.