GATE 2023 CE (CE2) – Question 47

Correct answer: (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

Explanation

Check each statement.

• **A. Turbulent boundary-layer thickness $\propto\sqrt x$.** False. The $\sqrt x$ law is for the **laminar** boundary layer ($\delta\propto x/\sqrt{Re_x}$). For the turbulent layer $\delta\propto x^{4/5}$ ($\delta/x\propto Re_x^{-1/5}$).
• **B. Interchanging a source's streamlines and equipotential lines gives a sink.** False. Interchanging them turns radial streamlines into circles, which is a **free vortex**.
• **C. Vertical force on a curved surface equals the weight of the liquid above it.** True: the vertical component is the weight of the liquid column (real or imaginary) vertically above the surface up to the free surface. ✓
• **D. Momentum correction factor for laminar pipe flow is larger than for turbulent.** True. For laminar flow $\beta=4/3\approx1.33$, while for turbulent flow it is only slightly above 1 (about 1.01 to 1.05). ✓

Correct: **C and D**.