A laminar plane jet of water issues from a nozzle of width at speed (water properties: , )

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 laminar plane jet of water issues from a nozzle of width b=0.40 mmb = 0.40\,\mathrm{mm} at speed U0=0.25 m s−1U_0 = 0.25\,\mathrm{m\,s^{-1}} (water properties: ρ=998 kg m−3\rho = 998\,\mathrm{kg\,m^{-3}}, μ=1.00×10−3 Pa s\mu = 1.00\times10^{-3}\,\mathrm{Pa\,s}). The similarity solution for a laminar plane jet gives a centreline speed that falls as x−1/3x^{-1/3} with distance xx downstream. ((a)) Compute the Reynolds number Re=U0b/νRe = U_0 b/\nu of the jet at the nozzle and confirm it is consistent with laminar flow. ((b)) The centreline speed is measured to be 0.15 m s−10.15\,\mathrm{m\,s^{-1}} at x1=2.0 cmx_1 = 2.0\,\mathrm{cm} from the nozzle. Predict the centreline speed at x2=8.0 cmx_2 = 8.0\,\mathrm{cm}.

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