Thickness of the boundary layer in turbulent flow :

$$\frac{\delta}{x} = \frac{0.376}{Re_x^{1/5}} = \frac{0.376}{\left(\frac{\rho u_{\infty}x}{\mu}\right)^{1/5}}$$

$$\delta = \frac{0.376x^{4/5}}{\left(\frac{\rho u_{\infty}}{\mu}\right)^{1/5}}$$

Therefore, $$\delta \propto x^{4/5}$$

The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is not proportional to the square root of the distance from the leading edge.

Therefore, option A is incorrect.

If the streamlines and equipotential lines of a source are reversed (change direction), the resulting flow will be a sink.

Therefore, option B is correct.

GATE CE 2023 Set 2 Fluid Mechanics and Hydraulic Machines - Boundary Layer Theory Question 1 English Explanation

For a curved surface immersed in a stationary liquid, the vertical component of the force on the curved surface is :

PH: The total pressure on the vertical plane's projected area of the curved surface. PH acts at the center of pressure of the plane surface and is equal to the entire pressure that the liquid exerts on an imaginary vertically submerged plane surface, which is the vertical projection of the curved surface.
Pv : The weight of the liquid inside the section that rises vertically above the curved surface and reaches the liquid's free surface.

Therefore, P_V will operate through the liquid's center of gravity in the section that extends above the curved surface and up to the liquid's free surface (represented by the profile ABCDEFA).

Therefore, option C is correct.

For flow through circular pipes, the momentum correction factor for laminar flow is always larger than that for turbulent flow.

Therefore, option D is correct.

Boundary Layer Theory · Fluid Mechanics and Hydraulic Machines · GATE CE

Marks 2