Introduction:
When a smooth flat rectangular plate is placed edgewise in a stream of fluid, it experiences a drag force due to the fluid flow. The drag force can be divided into two components: the drag force on the front portion and the drag force on the rear portion. We are required to find at what fraction of the length from the leading edge would the drag force on the front portion be equal to half of the total drag force.

Explanation:
To solve this problem, we can use the concept of the drag coefficient and the drag force equation for a flat plate in laminar flow.

Drag Coefficient:
The drag coefficient (Cd) is a dimensionless quantity that represents the drag force experienced by an object in a fluid flow. For a smooth flat plate in laminar flow, the drag coefficient can be determined using the following equation:

Cd = (1.328 / Re) + (0.424 / Re^0.5) + (0.032 / Re^0.6)

Where Re is the Reynolds number, defined as the ratio of inertial forces to viscous forces and can be calculated as:

Re = (ρ * V * L) / μ

Where ρ is the fluid density, V is the velocity of the fluid, L is the characteristic length, and μ is the dynamic viscosity of the fluid.

Drag Force Equation:
The drag force (Fd) on a flat plate can be calculated using the following equation:

Fd = 0.5 * Cd * ρ * V^2 * A

Where Cd is the drag coefficient, ρ is the fluid density, V is the velocity of the fluid, and A is the projected area of the plate normal to the flow direction.

Calculating the Fraction:
To find 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 can compare the drag forces on the front and rear portions of the plate.

Let's assume that the total length of the plate is L. We need to find the fraction x at which the drag force on the front portion (Lf) is equal to half of the total drag force (Lt).

Lf = 0.5 * Lt

Using the drag force equation, we can write:

0.5 * Cd * ρ * V^2 * Af = Cd * ρ * V^2 * At

Where Af is the projected area of the front portion and At is the projected area of the total plate.

Simplifying the equation, we get:

0.5 * Af = At

Since the length of the front portion is xL, and the length of the rear portion is (1-x)L, we can write:

Af = xL * B

At = L * B

Where B is the width of the plate.

Substituting these values into the equation, we get:

0.5 * xL * B = L * B

Simplifying the equation, we get:

x = 0.5

Therefore, 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 is 0.5 or 50%.