Question

Bernoulli's principle is applicable to

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

Hint:

Ideal Fluid = Non-viscous + Incompressible + Streamline Flow.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question asks for the conditions under which Bernoulli's principle is valid. Bernoulli's principle is a statement of the conservation of energy for a moving fluid.
Step 2: Detailed Explanation:
Bernoulli's equation is derived based on several key assumptions about the fluid and its flow. These assumptions define the ideal conditions for which the principle holds true. Let's break them down: 1. Streamline (or Laminar) Flow: The fluid particles must follow smooth paths (streamlines) without any eddies or chaotic motion. The principle is not applicable to turbulent flow. 2. Incompressible Fluid: The density of the fluid must remain constant. This is a good approximation for most liquids and for gases at low speeds, but not for gases at high speeds. 3. Non-viscous Fluid: Viscosity is the internal friction in a fluid. The derivation of Bernoulli's principle assumes there are no energy losses due to viscous forces. Therefore, the fluid must be non-viscous (an idealization). 4. Steady Flow: The velocity, pressure, and density at any point in the fluid do not change with time. Combining these key conditions, Bernoulli's principle is applicable to non-viscous, incompressible fluids in streamline flow.
Step 3: Final Answer:
The correct set of conditions is given in option (A).