Laminar or Turbulent Boundary Layer?
An aluminum canoe moves horizontally along the surface of a lake at 3.5 mi/h (Fig. 10–84). The temperature of the lake water is 50°F. The bottom of the canoe is 20 ft long and is flat. Is the boundary layer on the canoe bottom laminar or turbulent?
SOLUTION We are to assess whether the boundary layer on the bottom of a canoe is laminar or turbulent.
Assumptions 1 The flow is steady and incompressible. 2 Ridges, dings, and other nonuniformities in the bottom of the canoe are ignored—the bottom is assumed to be a smooth flat plate aligned exactly with the direction of flow. 3 From the frame of reference of the canoe, the water below the boundary layer under the canoe moves at uniform speed V = 3.5 mph.
Properties The kinematic viscosity of water at T=50^{\circ} F \text { is } v=1.407 \times 10^{-5} ft²/s.
Analysis First, we calculate the Reynolds number at the stern of the canoe,
Re _{x}=\frac{V x}{v}=\frac{(3.5 mi / h )(20 ft )}{1.407 \times 10^{-5} ft ^{2} / s }\left(\frac{5280 ft }{1 mi }\right)\left(\frac{1 h }{3600 s }\right)=7.30 \times 10^{6}
Since Re _{x} is much greater than \operatorname{Re}_{x, cr }\left(5 \times 10^{5}\right), and is even greater than \operatorname{Re}_{x, \text { transition }}\left(50 \times 10^{5}\right), the boundary layer is definitely turbulent by the back of the canoe.
Discussion Since the canoe bottom is neither perfectly smooth nor perfectly flat, and since we expect some disturbances in the lake water due to waves, the paddles, swimming fish, etc., transition to turbulence is expected to occur much earlier and more rapidly than illustrated for the ideal case in Fig. 10–81. Hence we are even more confident that this boundary layer is turbulent.
