Analogous to the planar jet in Example 9.3-2 is one that emerges from a circular opening. The boundary-layer momentum equation for an axisymmetric flow is

and the kinematic momentum is defined now as

(a) Show that K is constant. (Integrate the momentum equation from r = 0 to r = ∞ and use integration by parts to evaluate the contribution from v_r∂v_z/∂r.)

(b) Assuming that K is specified, obtain OM estimates for the jet radius δ(z), the maximum velocity v_m(z), and the volume flow rate Q(z). For comparison, the exact result for the flow rate is

(Schlichting, 1968, p. 221). Notice that, although K is the measure of jet strength, it does not affect Q.

Transcribed Image Text:

Vr avz ar avz +uz = дz га rar auz ar (P9.9-1)