Question

Bernoulli's equation is applicable in the case of

• A. Compressible liquid with streamline flow
• B. Compressible liquid with turbulent flow
• C. Incompressible liquid with streamline flow
• D. Incompressible liquid with turbulent flow

Hint:

Remember the four primary assumptions required for Bernoulli's Equation to apply:
1. Steady flow
2. Incompressible fluid
3. Non-viscous (inviscid) fluid
4. Flow along a streamline

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Bernoulli's equation represents the principle of conservation of energy applied to a flowing fluid. It states that the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along any streamline of the flow.
Key Formula or Approach:
The standard mathematical expression of Bernoulli's equation is: \[ P + \frac{1}{2}\rho v^2 + \rho g z = \text{constant} \]

Step 2: Detailed Explanation:
The derivation of Bernoulli's equation from Euler's equation of motion relies on several simplifying assumptions:

Incompressible Fluid: The density (\(\rho\)) of the fluid must remain constant throughout the flow. This assumption is generally valid for liquids.

Inviscid (Non-viscous) Fluid: The fluid is assumed to have zero viscosity, meaning there are no shear stresses or energy losses due to friction.

Steady Flow: The velocity, pressure, and density at any fixed point in the flow field do not change over time.

Streamline Flow: The fluid particles move along smooth, orderly paths called streamlines. The flow must not be turbulent, as turbulent flow introduces chaotic eddies and significant energy dissipation that violates the simple conservation relationship.
Thus, Bernoulli's equation is applicable for an incompressible liquid experiencing steady, streamline flow.

Step 3: Final Answer:
Bernoulli's equation is applicable to an incompressible liquid with streamline flow, which corresponds to Option (C).