The problem states that a flat smooth rectangular plate is placed edgewise in a stream of fluid, and we need to determine the fraction of the length from the leading edge at which the drag force on the front portion is equal to half of the total drag force. We are also given that the boundary layer is laminar.


To solve this problem, we need to understand the concepts of drag force and boundary layer.

- Drag Force: The drag force is the resistance force experienced by an object when it moves through a fluid. It is caused by the interaction between the object and the fluid, resulting in a net force opposing the motion of the object.

- Boundary Layer: The boundary layer is the thin layer of fluid that forms on the surface of an object when it moves through a fluid. It is characterized by a gradual transition of flow velocity from the free stream to zero at the surface of the object. The boundary layer can be laminar or turbulent, depending on the fluid flow conditions.


To determine the fraction of the length from the leading edge at which the drag force on the front portion is equal to half of the total drag force, we need to consider the distribution of drag force along the length of the plate.

- The drag force experienced by a flat plate in a fluid flow is given by the equation:

Fd = 0.5 * ρ * V^2 * Cd * A

Where Fd is the drag force, ρ is the density of the fluid, V is the velocity of the fluid, Cd is the drag coefficient, and A is the reference area of the plate.

- The drag coefficient depends on the shape of the object and the flow conditions. For a flat plate in laminar flow, the drag coefficient is given by:

Cd = 1.328 / Re^0.5

Where Re is the Reynolds number, which is a dimensionless parameter that characterizes the flow regime. For laminar flow over a flat plate, Re is given by:

Re = (ρ * V * L) / μ

Where L is the length of the plate and μ is the dynamic viscosity of the fluid.

- We can assume that the drag force distribution along the length of the plate is linear. Therefore, the drag force on the front portion of the plate is equal to half of the total drag force when the distance from the leading edge is equal to half of the length of the plate.

Fraction = 0.5 * L / L = 0.5

Therefore, the correct answer is option 'B' 1/2.