Question

The continuity equation \[ \frac{du}{dx} + \frac{dv}{dy} + \frac{dw}{dz} = 0 \] is valid only for:

• A. Ideal fluid flow
• B. Incompressible fluid
• C. Steady flow and incompressible fluids
• D. Steady flow and compressible fluids

Hint:

The general continuity equation applies to steady flow and compressible fluids, where density changes are considered in the mass conservation.

Answer 1

The Correct Option is D

The given continuity equation is the general form of the continuity equation for fluid flow, which describes the conservation of mass. The equation is valid for steady and compressible fluids, meaning that the fluid's density can change with time and location, but the mass remains conserved.
- Ideal fluid flow assumes no viscosity or compressibility, but the continuity equation applies for a broader set of fluids.
- Incompressible fluids also satisfy the continuity equation, but only for cases where the fluid's density does not change, typically used in low-speed flow situations.
- Steady flow and incompressible fluids would work for a simplified version of the continuity equation, but not for the general form where compressibility is allowed.
Thus, the general form of the continuity equation is valid for steady flow and compressible fluids, making option (4) the correct answer.