Question

Bernoulli's equation is applicable under which of the following conditions?

• A. Only for compressible flows
• B. When thermal energy changes are significant
• C. In inviscid, steady, and incompressible flows
• D. Only in turbulent flows

Hint:

Bernoulli Equation Assumptions. Valid for flow that is: Steady, Incompressible, Inviscid (frictionless), and along a streamline.

Answer 1

The Correct Option is C

Bernoulli's equation (\( P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant} \) along a streamline) is a statement of energy conservation for fluid flow, derived from Euler's equation.
Its derivation relies on several key assumptions about the flow:
(1) Inviscid: The fluid must have zero viscosity (no frictional losses).

(2) Steady: Fluid properties (velocity, pressure, density) at any point do not change with time.

(3) Incompressible: The fluid density (\(\rho\)) is constant.

(4) Flow is along a streamline (or the flow is irrotational).
Option (3) lists the main conditions: inviscid (no friction), steady, and incompressible.
Compressible flows (Option 1), significant thermal changes (Option 2), and turbulent flows (Option 4, which is inherently viscous and unsteady) violate the core assumptions of the standard Bernoulli equation.