(C) For a curved surface immersed in a stationary liquid, the vertical component of the force on the curved surface is equal to the weight of the liquid above it; (D) For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow
Solution
1.Statement (A): For a turbulent boundary layer over a flat plate, the thickness δ is given by δ≈Rex1/50.37x∝x4/5. For a laminar boundary layer, δ∝x1/2. The statement claims δ∝x for turbulent flow, which is incorrect.
2.Statement (B): Interchanging the streamlines and equipotential lines of a source results in a free vortex flow. A sink is simply a source with a negative strength. Thus, (B) is incorrect.
3.Statement (C): The vertical component of the hydrostatic force on a curved surface is equal to the weight of the liquid volume vertically above the surface extending to the free surface. This is a standard principle in hydrostatics. Thus, (C) is correct.
4.Statement (D): The momentum correction factor (β) is defined as β=AV21∫u2dA. For laminar flow in a circular pipe, β=4/3≈1.33. For turbulent flow, β is much closer to 1 (typically 1.01 to 1.05). Therefore, βlaminar>βturbulent. Thus, (D) is correct.
