Explanation:
The thickness of turbulent boundary layer at a distance x from the leading edge over a flat plate varies as x^4/5.

- Turbulent boundary layer: The region of fluid flow over a surface where the velocity of the fluid particles is influenced by the surface friction is called the boundary layer. In case of turbulent flow, the velocity of fluid particles is highly irregular and fluctuates in magnitude and direction.
- Flat plate: A flat plate is a two-dimensional object with a uniform thickness and width. It is used as a model to study the fluid flow over surfaces.
- Thickness of boundary layer: The thickness of the boundary layer is the distance between the surface and the point where the velocity of the fluid particle reaches 99% of the free stream velocity.
- Variation of thickness with distance: The thickness of the boundary layer increases with distance from the leading edge of the flat plate. The variation of thickness with distance is given by x^m, where m is a constant that depends on the type of flow (laminar or turbulent).
- Empirical formula for turbulent flow: In case of turbulent flow over a flat plate, the empirical formula for the variation of thickness with distance is given by x^4/5. This means that the thickness of the turbulent boundary layer increases faster with distance compared to the laminar boundary layer.
- Importance of boundary layer: The boundary layer has a significant impact on the drag force experienced by the object. A thicker boundary layer results in higher drag force due to increased surface friction.

Therefore, the correct option is C. x^4/5.

Thickness for a turbulent flow if velocity distribution of (u/U)=(y/∆)^(1/7) is given as
∆=0.371x/(Re)^(1/5)
here Re is the local Reynolds number at dist x from leading edge and given as Re=(U×x)/v
ignoring constants we get relation as
∆--- x/(x^1/5)==x^(1-1/5)==[x^(4/5)]