Question

Continuity equation of fluid flow is

• A. Law of conservation of energy
• B. Law of conservation of mass
• C. Law of conservation of momentum
• D. Law of conservation of pressure

Hint:

Conservation Principles in Fluids:
Continuity Equation $\rightarrow$ Conservation of Mass.
Bernoulli Equation $\rightarrow$ Conservation of Energy.
Momentum Equation $\rightarrow$ Conservation of Momentum (Newton's 2nd Law).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The continuity equation is the mathematical statement expressing the principle of conservation of mass in fluid mechanics.
Key Formula or Approach:
\[ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0 \]
\[ A_1 v_1 = A_2 v_2 = Q \quad \text{(for 1D steady incompressible flow)} \]

Step 2: Detailed Explanation:
The continuity equation states that in a closed fluid system with no internal sources or sinks:
The mass entering a control volume per unit time must exactly equal the mass leaving the control volume plus the rate of mass accumulation within the control volume.
For steady, incompressible flow:
\[ \rho_1 A_1 v_1 = \rho_2 A_2 v_2 \implies A_1 v_1 = A_2 v_2 \]
This is a direct expression of the Law of Conservation of Mass.

Step 3: Final Answer:
Therefore, the continuity equation represents the Law of conservation of mass, matching option (B).