# Calculation Methods - Centrifugal Pump

The performance curves for centrifugal pumps are usually expressed as simple polynomials, as a series of cubic splines or in some instances as Chebyshev polynomials. FluidFlow uses this approach to store the performance data. For a simple polynomial the expression is Δ H = C 1 + C 2 Q + C 3 Q 2 + C 4 Q 3 ..... The performance data in situ is adjusted according to any or all of the following factors. 1. A change in operating speed or impeller size, from that provided in the pump database. If this occurs the pump performance data is adjusted according to the affinity laws: Q 1/Q 2 = (N 1/N 2) (D 1/D 2) H 1/H 2 = (N 1/N 2)2 (D 1/D 2)2 NPSHr 1/NPSHr 2 = (N 1/N 2)2 (D 1/D 2)2 P h1/P h2 = (N 1/N 2)3 (D 1/D 2)3 where: Q is the volumetric flow rate. N is the pump speed (RPM). D is the impeller diameter. H is the pressure or head developed by the pump. Ph is the shaft power. NPSHr is the net positive suction head requirement. 2. If a liquid with a viscosity higher than 4.3 centistokes is encountered then FluidFlow makes a correction to the performance data according to the method described in the Hydraulic Institute Standards. This correction will only occur if the option has been enabled from the "Global Settings Tab" of the Calculation Options dialog. 3. If a slurry is being pumped and derating has been set from the Input Editor then the performance data will be adjusted according to the adjustment method selected. FluidFlow displays the Pump Shaft Power in the calculated results. The Pump Shaft Power is calculated from the hydraulic power and the pump efficiency at the duty point. This is given by the formula: P h = Q ρ g H / η The following example provides an illustration of how the Pump Shaft Power is calculated. Note, this model can be opened from the following path: "[FluidFlow3 folder]\QA Incompressible Flow\Boosters\4 Pumps in Parallel 3 Operating.ff3". Figure 1: Pump Shaft Power. If we consider centrifugal pump node 11, we can calculate the Pump Hydraulic Power from: Q*rho*g*H/3.6 *10 6. Pump Hydraulic Power = 36.3913355186*999.0905263535*9.80665*24.9323675717/3.6 *106 = 8889698.49111202/3.6 *106 = 2.46936069 kW. The Pump Shaft Power can now be determined by dividing the Pump Hydraulic Power by the efficiency (η). Pump Shaft Power = 2.46936069 / 0.7093 = 3.4814 kW. See the Nomenclature section for the symbol definitions.