To appreciate why laminar flow is of minimal importance in m

To appreciate why laminar flow is of minimal importance in many engineering applications, compute the percent of the vehicle over which laminar flow exists for the following situations. In each case, consider the boundary layer on a flat portion of the vehicle and assume transition occurs at a Reynolds number of 5 times 10^5. A 20-foot automobile moving at 25 mph (1.62 times 10^-4 ft^2/sec). A 20-foot automobile moving at 65 mph (1.62 times 10^-4 ft^2/sec). A small aircraft with a wing chord length of 8 feet moving at 150 mph (1.67 times 10^-4 ft^2/sec).

Solution

Given,

Transition Reynolds number = 5 X 10⁵

a.

Given,

We know that,

The transition Reynolds number: Re = U_*x_tr/ = 5 x 10⁵ ……………………..(I)

Therefore solving above equation we get,

x_tr = 2.21 feet

So percent of vehicle over which laminar flow exists = x_tr / L = 11.05 %

Similarly,

b.

Given,

Therefore solving equation (I) we get,

x_tr = 0.85 feet

So percent of vehicle over which laminar flow exists = x_tr / L = 4.25 %

c.

Given,

Therefore solving above equation (I) we get,

x_tr = 0.379 feet

So percent of vehicle over which laminar flow exists = x_tr / L = 4.74 %