**Problem Statement:**
A smooth plate with dimensions 2 m wide and 2.5 m long is towed in oil (specific gravity = 0.8) at a velocity of 1.5 m/s along its length. Find the thickness of the boundary layer at the trailing edge of the plate, given that the oil viscosity is 10^-4 m/s.

**Solution:**

To find the thickness of the boundary layer at the trailing edge of the plate, we can use the concept of boundary layer theory. The boundary layer is a thin layer of fluid that develops near the surface of an object moving through a fluid. In this case, the fluid is oil and the object is a smooth plate.

**Step 1: Calculate the Reynolds number:**

The Reynolds number (Re) is a dimensionless parameter that characterizes the flow of a fluid. It is given by the formula:

Re = (ρ * V * L) / μ

where:
- ρ is the density of the fluid (oil)
- V is the velocity of the plate along its length
- L is the characteristic length of the plate (width or length in this case)
- μ is the dynamic viscosity of the fluid (oil)

Given:
- V = 1.5 m/s
- L = 2 m (width of the plate)
- ρ = specific gravity * density of water (since specific gravity = 0.8, density of water = 1000 kg/m³)
- μ = 10^-4 m/s

Let's calculate the Reynolds number:

ρ = 0.8 * 1000 kg/m³ = 800 kg/m³

Re = (800 * 1.5 * 2) / (10^-4)
Re = 24,000,000

**Step 2: Determine the type of flow:**

Based on the Reynolds number, we can determine the type of flow. The flow can be classified into three categories:

1. Laminar flow: Re < />
2. Transitional flow: 2000 < re="" />< />
3. Turbulent flow: Re > 4000

In this case, Re = 24,000,000, which indicates turbulent flow.

**Step 3: Calculate the boundary layer thickness:**

For turbulent flow, the boundary layer thickness can be estimated using the empirical Blasius equation:

δ = 5 * (x / Re^(0.5))

where:
- δ is the boundary layer thickness
- x is the distance from the leading edge of the plate
- Re is the Reynolds number (in this case, Re = 24,000,000)

To find the thickness of the boundary layer at the trailing edge of the plate, we need to calculate the distance x from the leading edge to the trailing edge.

Given:
- Length of the plate = 2.5 m

Since the plate is towed at a velocity of 1.5 m/s along its length, the trailing edge is 2.5 m away from the leading edge.

x = 2.5 m

Let's calculate the boundary layer thickness at the trailing edge:

δ = 5 * (2.5 / 24,000,000^(0.5))
δ ≈ 0.06455 m

Converting the thickness to millimeters:

δ = 0.06455