Question

What is the value of kinetic energy thickness?

(a) δ^** = \(\int_0^∞ \frac {u}{U_e}\big [  \)1 – \(\big ( \frac {u}{U_e}\big )^2 \big ] \)dy

(b) δ^** = \(\int_0^∞ \frac {u}{U_e} \big [  \)1 – \(\frac {u}{U_e}\big ] \)dy

(c) δ^** = \(\int_0^∞ \big [ \)1 – \(\frac {u}{U_e} \big ] \)dy

(d) δ^** = \(\int_0^∞ \frac {u}{U_e} \big [ \)1 + \(\frac {u}{U_e}\big ] \)dy

The question was posed to me by my school teacher while I was bunking the class.

My question comes from Boundary Layer Properties in portion Boundary Layers, Laminar & Turbulent Boundary Layers, Navier Stokes Solutions of Aerodynamics

Answer 1

Correct option is (a) δ^** = \(\int_0^∞ \frac {u}{U_e}\big [  \)1 – \(\big ( \frac {u}{U_e}\big )^2 \big ] \)dy

Best explanation: Kinetic energy thickness is the distance the boundary is displaced by in the perpendicular direction to compensate for the reduced kinetic energy of the fluid due to the formation of boundary layer. It is given by:

δ^** = \(\int_0^∞ \frac {u}{U_e}\big [  \)1 – \(\big ( \frac {u}{U_e}\big )^2 \big ] \)dy

Where, u is velocity at some point x on the plate.

Ue is the freestream velocity.