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'Q . PERFORMANCE MEASURES AND CALCULATIONS 24 mt is the total mass flow rate [lbm/secl vzS is the isentropic exhaust volme [cubic ft/lbml dhs is the isentropic enthalpy drop [ft-lbf/lbm'l D is the rotor diameter Cft] The specific speed and specific size as calculated have units of RPM(lbm-ft/lbf) 3/4/sec1/2 and (lbf/ (lbm-ft/sec2) 1/4* These parameters can be made unitless by multipl ication by unit constants: respectively Ns = ns (7.75 1E-3 (rad-mid rev-sec) (lbf/ (lbm-ft/sec2) 314 D, = d s ( 2 . 3 8 2 ( ( l b m - f t / s e c 2 ) / l b f 1 1 1 4 1 There are six dimensional variables currently being considered in dimensional analysis: Power Total Mass Flow Rate Isentropic Enthalpy Drop(Head1 Engine Speed Engine Size(Rotor Diameter) Isentropic Exhaust Volume These six dimensional variables are described by three fundamental dimensions: mass, l e n g t h and time. The Buckingharn-Pi Theorm[lOl states that there are then 6 - 3 = 3 independent dimensionless groupings of the dimensional variables. Along with efficiency, the specific speed and specific size comprise one set of 3 independent dimensionless groups. Other possible dimensionless groups include: the specific power PR = (POWER)(V2s) / (N3D5) the dh e nsi0nless head t h e dimensionless flow H* = dh, / (N2D2) F*= (1ntv2~)/ (ND3) the specific momentum M* = POMER / (Nhtdhsl/2) Also, it has been suggested that for power devices, the power specific speed(Nsp) and power specific size(Dsp) may bePDF Image | EMPIRICAL MODELING OF A LYSHOLM HELICAL SCREW EXPANDER
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