Question

What is the equation for momentum 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 asked during an interview.

Question is taken from Boundary Layer Properties topic in section Boundary Layers, Laminar & Turbulent Boundary Layers, Navier Stokes Solutions of Aerodynamics

Answer 1

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

The explanation: Within the boundary layer, momentum thickness is described in relation to the momentum flow rate. This rate is lower than that which would occur if there were no boundary layer, when the velocity would be equal to the mainstream velocity Ue in the vicinity of the surface considered at the station.

It is given by:

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

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

Ue is the freestream velocity.