Question

Consider the boundary layer next to the smooth hull of a ship. The ship is cruising at a speed of 45 ft/s in 60 degree F fresh water. Assuming that the boundary layer on the ship hull develops the same as on a flat plate, determine: The thickness of the boundary layer at a distance x = 100 ft downstream from the bow. The shear stress, tau_0, adjacent to the hull at x = 100 ft.

Answer 1

The thickness of the boundary layer at a distance of 100 ft downstream from the bow is approximately 0.003 ft. The shear stress adjacent to the hull at x = 100 ft is approximately 421.6 lb/ft².

Step-by-step explanation:

The thickness of the boundary layer at a distance of 100 ft downstream from the bow can be determined using Prandtl's boundary layer thickness formula:

δ = 5.0 * sqrt((ν * x) / U)

Where:

δ is the boundary layer thickness

ν is the kinematic viscosity of water (1.139 * 10^-6 ft^2/s at 60°F)

x is the distance from the start of the boundary layer (100 ft)

U is the velocity of the flow (45 ft/s)

Plugging in the values, we can calculate:

δ = 5.0 * sqrt((1.139 * 10^-6 * 100) / 45) = 0.003 ft

So, the thickness of the boundary layer at a distance of 100 ft downstream from the bow is approximately 0.003 ft.

The shear stress, τ0, adjacent to the hull at x = 100 ft can be calculated using the equation:

τ0 = 0.332 * ρ * U^2

Where:

τ0 is the shear stress

ρ is the density of water (62.428 lb/ft³ at 60°F)

U is the velocity of the flow (45 ft/s)

Plugging in the values, we can calculate:

τ0 = 0.332 * 62.428 * 45^2 = 421.6 lb/ft²

So, the shear stress adjacent to the hull at x = 100 ft is approximately 421.6 lb/ft².