Question

The flow of an incompressible fluid is described by the Bernoulli equation. Which of the following quantities is not conserved along a streamline in steady flow?

• A. Pressure
• B. Kinetic energy
• C. Potential energy
• D. Volume flow rate

Hint:

Bernoulli’s equation is useful for analyzing fluid dynamics but does not account for volume flow rate conservation along a streamline.

Answer 1

The Correct Option is D

The Bernoulli equation describes the behavior of an incompressible fluid flow along a streamline. The equation states that the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline in steady flow.
Step 1: The Bernoulli equation is: \[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \] where:
\( P \) is the pressure,
\( v \) is the velocity of the fluid,
\( \rho \) is the fluid density,
\( g \) is the acceleration due to gravity,
\( h \) is the height (potential energy).
Step 2: The equation shows that pressure, kinetic energy, and potential energy are all conserved along a streamline in steady flow. The volume flow rate (which involves the total flow through a pipe or duct) is not directly conserved along a streamline in this equation. Thus, the correct answer is Volume flow rate.