Question

Problem 1: Boundary Layer (6 points) (a) A small 15-mm long fish swims with a speed of 20 mm/s. Would a boundary layer type flow be developed along the sides of the fish? Explain. Hint: Re numbers>1000 are needed for boundary layer type flow. (b) An aluminum canoe moves horizontally along the surface of a lake at 5.0 mph. The temperature of the water is 50°F. The bottom of the canoe is 16 feet long and is flat. Is the boundary layer on the canoe bottom laminar or turbulent?

Answer 1

(a) l = 15 mm = 0.015 m v = 20 mm/s = .02 m/s Re = rho v l/mu Fish swims in the water (rho i = 1000 log/m^2) mu/rho = epsilon = 1.12 times 10^-6 m^2/s at 15.5 degree C of water Re = rho v l/mu = v l/upslion Re = .02 times .015/1.12 times 10^-6 = 268 This is not large enough to have true boundary layer type flow: as Re 1000 is often the lower limit. So, a boundary layer type flow cannot be developed along the sides of the fish. V = .5 mph = 2.2352 m/s (1 mph = .44704 m/s) L = 16 ft = 16 times .3048