Question

Which of the following statements is/are TRUE?

• A. The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the square root of the distance from the leading edge
• B. If the streamlines and equipotential lines of a source are interchanged with each other, the resulting flow will be a sink
• 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

Hint:

For boundary layer thickness in turbulent flow, remember that the square root law is for laminar flow. Also, momentum correction factors are higher for laminar flow due to its parabolic velocity profile.

Answer 1

The Correct Option is C, D

Statement (A): The thickness of a turbulent boundary layer is indeed proportional to the square root of the distance from the leading edge. However, this relation holds for laminar flow and not necessarily for turbulent flow. Thus, Statement (A) is False.
Statement (B): If the streamlines and equipotential lines of a source are interchanged, the flow does not become a sink. A source and a sink are distinct flow patterns, and interchanging streamlines and equipotential lines would not convert a source into a sink. Thus, Statement (B) is False.
Statement (C): For a curved surface immersed in a stationary liquid, the vertical component of the force is indeed equal to the weight of the liquid above the surface, which is derived from hydrostatic pressure. Thus, Statement (C) is True.
Statement (D): For flow through circular pipes, the momentum correction factor for laminar flow is indeed larger than that for turbulent flow, as laminar flow has a parabolic velocity profile, while turbulent flow has a flatter profile. Thus, Statement (D) is True.
\[ \boxed{\text{Correct Statements: (C) and (D)}} \]