n = Kinematic viscosity (cst) SG = specific gravity or 1 Poise = 100 cp 1 Stoke = 100 cst Q = capacity (m 3 /s) A = tube area (m 2 ) or

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1 Fmulas Designation Fmula Comments Product Viscosity n = m r n = Kinematic viscosity (mm /s) m = Absolute viscosity (mpa.s) n = m SG n = Kinematic viscosity (cst) m = Absolute viscosity (cp) m = n SG 1 Poise = 100 cp 1 Stoe = 100 cst Flow Velocity V = Q A A = tube area (m ) V = Q Q = capacity (m 3 /h) V = Q V = Q Reynolds number Re = D V r (ratio of inertia m D = tube diameter (m) fces to viscous fces) r = density (g/m³) m = absolute viscosity (Pa.s) Re = D V r m r = density (g/m³) m = absolute viscosity (cp) Re = 130 Q D m Q = capacity (l/min) m = absolute viscosity (cp) 1 JEC Pump

2 Designation Fmula Comments Reynolds number (ratio of inertia Re = 316 Q fces to viscous D n fces) n = inematic viscosity (cst) Re = 3800 Q D n n = inematic viscosity (cst) Pressure/Head Pressure (total fce P = F per unit area eerted A F = Fce by a fluid) A = Area Static Pressure/Head P = r g h (relationship between P = pressure/head (Pa) pressure and elevation) g = acceleration due to gravity (m/s ) h = height of fluid (m) P = h SG 10 P = pressure/head (bar) h = height of fluid (m) P = h SG.31 P = pressure/head (psi) h = height of fluid (ft) Total head H = H t (± H s ) H t = total discharge head H s = total suction head Total discharge head H t = h t + h ft + h t = static discharge head h ft = pressure drop in discharge line > 0 f pressure < 0 f vacuum = 0 f open tan Total suction head H s = - + (± ) = static suction head > 0 f flooded suction < 0 f suction lift = pressure drop in suction line > 0 f pressure < 0 f vacuum = 0 f open tan Friction loss Pf = L r V² (Miller equation) D Pf = friction loss (Pa) = friction fact (Darcy) L = tube length (m) D = tube diameter (m) JEC Pump

3 Designation Fmula Comments Friction loss (Miller equation) Pf = 5 SG L V² D Pf = friction loss (bar) = friction fact (Darcy) L = tube length (m) Pf = SG L V² D Pf = friction loss (psi) = friction fact (Darcy) L = tube length (ft) Darcy friction fact = 64 Re = friction fact Re = Reynolds number NPSHa (Net Positive NPSHa = Pa ± Pvp Suction Head (+ f flooded suction) Pa = pressure absolute above fluid level available) ( f suction lift) (bar) = static suction head (m) = pressure drop in suction line (m) Pvp = vapour pressure (bar a) Pa = pressure absolute above fluid level (psi) = static suction head (ft) = pressure drop in suction line (ft) Pvp = vapour pressure (psia) Power Hydraulic power Power (W) = Q H r g (theetical energy required) H = total head (m) g = acceleration due to gravity (m/s ) Power (W) = Q H Q = capacity (l/min) H = total head (bar) = 600 Power (hp) = Q H H = total head (psi) = 1715 Power (hp) = Q H H = total head (psi) = JEC Pump

4 Designation Fmula Comments Required power Hydraulic power (power needed at Efficiency (100% = 1.0) the pumhaft) Tque Tque Tque (Nm) = Required power (W) 9550 Tque (Kgfm) = Required power (W) 974 Tque (ftlb) = Required power (hp) 550 Efficiency Hydraulic efficiency Pump head loss (m) 100% (h h ) Total head (m)3 Mechanical 1 - Pump mech. losses 100% efficiency (h m ) Required power Volumetric efficiency = Q 100% (Centrifugal and Q + Q L = volumetric efficiency Liquid Ring pumps) Q = pump capacity Q L = fluid losses due to leaage through the impeller casing clearances Volumetric efficiency = Q 100% (Rotary Lobe pumps) q = volumetric efficiency Q = pump capacity q = pump displacement Pump efficiency Water hse power 100% (h p ) Required power h p = Q H r g w T h p = pump efficiency H = total head/pressure (m) g = acceleration due to gravity (m/s ) w = shaft angular velocity (rad/s) T = shaft tque (Nm) Overall efficiency Water hse power 100% (h oa ) Drive power JEC Pump 4

5 Designation Fmula Comments Pumpeed - Rotary Lobe Pump Pumpeed n = Q 100 q 60 q = pump displacement (m³/100 rev) n = Q 100 q q = pump displacement (US gall/100 rev) n = Q 100 q q = pump displacement (UK gall/100 rev) Flow Control - Centrifugal Pump and capacity and head and power Reduction of multi-stage impeller diameter capacity head power c-b a-b n n n 3 Q Q1 H H1 5 P P1 Q Q 1 H H1 3 P P1 D = (mm) D = (mm) H = head (m) D = (mm) P = power (W) D 1 = standard diameter (mm) a = ma. wing point (m) b = min. wing point (m) c = required wing point (m) H = head (m) P = power (W) 5 JEC Pump

PUMP SYSTEM ANALYSIS AND SIZING. BY JACQUES CHAURETTE p. eng.

PUMP SYSTEM ANALYSIS AND SIZING BY JACQUES CHAURETTE p. eng. 5 th Edition February 2003 Published by Fluide Design Inc. www.fluidedesign.com Copyright 1994 I TABLE OF CONTENTS Introduction Symbols Chapter