A round air jet issues from a nozzle of diameter at speed into still room air

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Separation, wakes, jets and free shear flows

Problem

A round air jet issues from a nozzle of diameter d=8.0 mmd = 8.0\,\mathrm{mm} at speed U0=25 m s−1U_0 = 25\,\mathrm{m\,s^{-1}} into still room air. The turbulent round jet's centreline speed follows the measured law Ucentre≈6(d/x)U0U_{\rm centre} \approx 6(d/x)U_0, and its volume (and so mass) flux grows linearly with x/dx/d, reaching about thirty-two times the nozzle flux at x/d=100x/d = 100. ((a)) Find the centreline speed at x=0.60 mx = 0.60\,\mathrm{m} from the nozzle. ((b)) Estimate the ratio of the local mass flux to the nozzle mass flux at this distance, assuming the same constant of proportionality that gives thirty-two at x/d=100x/d=100.

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