Fluid Mechanics

Step 1: Check each statement.
- (A) True: For irrotational flow, Bernoulli's equation applies universally in the flow field.
- (B) True: For rotational flow, the constant differs along different streamlines.
- (C) True: A nozzle reduces area, so velocity increases, leading to increased discharge.
- (D) True: With same head, nozzle increases velocity compared to a pipe without nozzle.

Step 2: Conclusion.
All four statements are correct Option (3).

Step 1: Recall definitions.
- Steady flow: Parameters (velocity, discharge) do not change with time.
- Non-uniform flow: Parameters vary with space (position).

Step 2: Analyze options.
- (1) Motion of river around bridge piers: Unsteady and complex (vortices, turbulence). Not purely steady non-uniform.
- (2) Steadily increasing flow through a pipe: This means unsteady (since velocity changes with time).
- (3) Steadily increasing flow through reducing section: Again indicates unsteady.
- (4) Constant discharge through tapering pipe: Flow is steady (constant with time), but velocity varies along pipe length (non-uniform). Correct.

Step 3: Conclusion.
Thus, the correct example of steady non-uniform flow is option (4).

Step 1: Recall definition of Reynolds number.
Reynolds number is:

Step 2: Check options.
- (1) Viscous/Inertia = Wrong (inverse of Reynolds).
- (2) Elastic/Pressure = Related to Mach number, not Reynolds.
- (3) Inertia/Viscous = Correct definition.
- (4) Gravity/Inertia = Related to Froude number, not Reynolds.

Step 3: Conclusion.
Hence, Reynolds number is the ratio of inertia force to viscous force.

Step 1: Recall the formula.
The head loss due to sudden enlargement in a pipe is given by:

Step 2: Explanation.
This is derived from applying Bernoulli's equation and considering the energy loss due to mixing of flows at the expansion section.

Step 3: Conclusion.
Thus, the correct formula for head loss due to sudden enlargement is .