Question

Bernoulli’s equation holds good for

• A. non-viscous and incompressible fluids in turbulent flow
• B. highly viscous and compressible fluids in streamline flow
• C. non-viscous and compressible fluids in turbulent flow
• D. highly viscous and incompressible fluids in streamline flow
• E. non-viscous and incompressible fluids in streamline flow

Hint:

Remember the mnemonic "NIS" for Bernoulli's assumptions: Non-viscous, Incompressible, Streamline.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Bernoulli's equation is a statement of the conservation of energy for flowing fluids. It is derived under several strict idealizing assumptions about the fluid and its flow.
Step 2: Key Formula or Approach:
Recall the theoretical conditions required to derive Bernoulli's Equation \(P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}\).
The required assumptions are: 1. Steady (streamline) flow. 2. Incompressible fluid (constant density). 3. Non-viscous (no internal friction/energy loss). 4. Irrotational flow.
Step 3: Detailed Explanation:
Let's evaluate the options based on the required assumptions:
(A) Turbulent flow invalidates the steady-flow assumption because velocity fluctuates unpredictably.
(B) Highly viscous fluids experience internal friction, causing kinetic energy to be lost as heat, violating energy conservation. Compressible fluids have varying density, breaking the basic form of the equation.
(C) Compressible fluids and turbulent flow violate the conditions.
(D) Highly viscous fluids violate the zero-friction requirement.
(E) Non-viscous (no energy loss), incompressible (constant density), and streamline (steady) flow perfectly match the ideal assumptions for Bernoulli's principle.
Step 4: Final Answer:
Bernoulli's equation holds good for non-viscous and incompressible fluids in streamline flow.