(a) Evaluate the scaling of the rate of mass flow (discharge) Ṁ(x) along the 3- dimensional turbulent jet of the previous exercise. Show that Ṁ increases with distance from the nozzle, so that mass must be entrained in the flow and become turbulent.

(b) Compare the entrainment rate for a turbulent jet with that for a laminar jet (Ex. 15.3). Do you expect the Coanda effect to be stronger for a turbulent or a laminar jet?

Data from Exercises 15.3.

Consider a narrow, 2-dimensional, incompressible (i.e., subsonic) jet emerging from a 2-dimensional nozzle into ambient fluid at rest with the same composition and pressure. (By 2-dimensionalwemean that the nozzle and jet are translation symmetric in the third dimension.) Let the Reynolds number be low enough for the flow to be laminar; we study the turbulent regime in Ex. 15.7.We want to understand how rapidly this laminar jet spreads.

Figure 15.4.

Transcribed Image Text:

jet jet ambient fluid at rest ambient fluid at rest w(x)