2013-3-6 Mass Flow Rate (One-Dimensional Flow) Flow is normal to the boundary at locations where mass enters or exits the control volume All intensive properties are uniform with position over each inlet or exit area(A) through which matter flows. Mi=PAV=AV (Eq.4c) 7) where V is velocity_(not volume v is specific volume 49 Mass Rate Balance (Steady-State Form) Steady-state:all properties are unchanging in time For steady-state control volume,di/dt=0. ∑m;=∑me 1 (Eq.4d) mass rate mass rate OUT For single stream (one input one output) devices:nozzles,turbines,compressors,pumps m=m。 or VA=,A Steady Incompressible flow(single stream) most liquids VA=V24 4-10 5 2013-3-6 5 Mass Flow Rate (One-Dimensional Flow) ►Flow is normal to the boundary at locations where mass enters or exits the control volume. ►All intensive properties are uniform with position over each inlet or exit area (A) through which matter flows. v AV m& = ρAV = (Eq. 4c) where V is velocity (not volume) v is specific volume 4-9 ►For single stream (one input & one output) devices: nozzles, turbines, compressors, pumps: ►Steady Incompressible flow (single stream) Æ most liquids Mass Rate Balance (Steady-State Form) ►Steady-state: all properties are unchanging in time ►For steady-state control volume, dmcv / dt = 0. (Eq. 4d) mass rate IN mass rate OUT 4-10 or ∑ = ∑ e e i m&i m& V1A1 =V2A2 mi me & = & ρ1 V1A1 = ρ 2 V2A2