Von Krmn assumed a cubic profile for the integral momentum analysis over a flat plate. Since a

Von Kármán assumed a cubic profile for the integral momentum analysis over a flat plate. Since a cubic has four constants, four conditions were used.

(i) \(V_{x}=0\) at \(y=0\).

(ii) \(V_{x}=V_{\mathrm{e}}\) at \(y=\delta\).

(iii) \(d V_{x} / d y=0\) at \(y=\delta\).

(iv) \(d^{2} V_{x} / d y^{2}=0\) at \(y=0\).

Show that the use of these conditions in a cubic profile leads to the representation given by Eq. (15.61).

Justify condition (iv) above using the \(x\)-momentum balance applied at \(y=0\) together with the no-slip boundry condition.

Transcribed Image Text:

12 2" 32 || (15.61)