Question

A hydrofoil which is 50 cm long moves in seawater at 20°C.

a)

If the plate is 5.6 m wide and moves at 32 knots, use the flat-plate theory with Re_tr= 5E5 to estimate its drag in N for a smooth wall. Round the final answer to the nearest whole number.

---------N

b)

If the hydrofoil is 5.6 m wide and moves at 32 knots, use the flat-plate theory with Re_tr = 5E5 to estimate its drag in N for a rough wall with ε = 0.3 mm. For seawater at 20°C, take ρ = 1025 kg/m³. Round the final answer to the nearest whole number.

------ N

Answer 1

Given that :

Length of hydrofoil = l = 50cm = 0.5 m

Width of hydrofoil = w = 5.6 m

Speed of hydrofoil = v = 32 knots (v = 16.45 m/s)

Density of sea water = d = 1025 kg/m^3

Viscosity of sea water = u = 0.00107 kg/m.s

Reynolds number = Re = 5E5

(a). Drag force (F) in N for a smooth wall

We know that drag force is F = (Cd*d*v^2*A)/2

Where Cd = coefficient of drag

A = area = 2×w×l =2×0.5×5.6 = 5.6 m^2

Cd = 0.031/(Re^1/7)-1440/Re

Reynolds number

Re = dvl/u = 1025×16.45×0.5/0.00107 = 7.8×10^6

Hence drag coefficient Cd = 0.00307

Drag force F = 0.00307×1025×(16.45^2)×5.6/2

Hence drag force F = 2384.25 N

(b). Drag force for a rough wall

Roughness of wall = ε = 0.3 mm

l/ε = 0.5/(0.3×10^(-3)) = 1666.7

Drag coefficient is given by

Cd = (1.89+1.62log(l/ε))^(-2.5) = 0.00742

Hence drag force for a rough wall is

F = 0.00742×1025×(16.45^2)×5.6/2 = 5,762.5885 N

Thank you!