Which of the following assumptions are used in Bernoulli’s equation? (1) Inviscid flow (2) Steady flow (3). Along a streamline (4). Compressible fluid
- A1, 2 and 3 onlyCorrect
- B1 and 3 only
- C2 and 4 only
- DAll of the above
Solution
Concept
Bernoulli's principle relates pressure, velocity, and elevation in a moving fluid based on the conservation of energy for an ideal fluid flow.
Formula
P/ρg + v²/2g + z = Constant
Step-by-step solution
1. Identify the standard assumptions for Bernoulli's equation: Steady flow, Incompressible flow, Irrotational flow, and Inviscid (frictionless) flow. 2. Evaluate the given statements: (1) Inviscid flow is correct. (2) Steady flow is correct. (3) Along a streamline is correct (unless the flow is irrotational, in which case the constant is the same everywhere). 4. Bernoulli's equation assumes an incompressible fluid (constant density), making 'Compressible fluid' incorrect. 5. Therefore, statements 1, 2, and 3 are correct, leading to option (A).
Explanation
Bernoulli's equation is derived from Euler's equation of motion by integration. It assumes the fluid is ideal (inviscid), the flow is steady and incompressible, and the analysis is performed along a single streamline.
Shortcut
Remember the mnemonic 'SI²': Steady, Incompressible, Inviscid, Irrotational.
Common mistake
Students often forget that Bernoulli's equation specifically requires an incompressible fluid (density remains constant).
Correct answer: A) 1, 2 and 3 only