Question

Which of the following equation must be perfunctorily satisfied while dealing with fluid flow problems?

• A. Newton’s third law
• B. Law of conservation of momentum
• C. Continuity equation
• D. Newton’s second law

Hint:

The continuity equation is your go-to equation for mass conservation — always check it first when analyzing fluid flows.

Answer 1

The Correct Option is C

In fluid mechanics, the continuity equation is a fundamental principle that expresses the conservation of mass.
This equation ensures that for any control volume (a defined region in space through which fluid may flow), the rate of mass entering the control volume must equal the rate of mass leaving it — assuming there is no accumulation or depletion of mass within the volume.
Mathematically, for an incompressible and steady flow, the continuity equation is written as:
\[ A_1 v_1 = A_2 v_2 \]
Where:
$A$ = cross-sectional area of flow
$v$ = flow velocity at the respective section
This equation must be satisfied in all fluid flow problems, regardless of whether the flow is steady or unsteady, compressible or incompressible.
Let’s assess the other options:
- (1) Newton’s third law — relates to action and reaction forces, important in mechanics but not directly used for analyzing fluid flow quantitatively.
- (2) Law of conservation of momentum — certainly relevant in fluid dynamics (e.g., Navier-Stokes equations), but not the most fundamental condition to check first.
- (4) Newton’s second law — applies to individual particles or rigid bodies, not directly used to verify mass conservation in flow.
Hence, the continuity equation is the one that must be satisfied in all fluid flow scenarios.