The Affinity Laws (also called the Fan Laws) state that fan output CFM or flow is directly proportional to the speed of the fan. Static pressure is proportional to the fan speed squared, and fan required HP is proportional to the fan speed cubed. Therefore, according to the Affinity Laws of speed, pressure, and horsepower, to produce 50% airflow, the fan would be run at 50% speed. At this operating point, the fan would produce 25% of rated pressure (0.5 x 0.5 = 0.25), and would require only 12.5% of rated horsepower (0.5 x 0.5 x 0.5 = 0.125 or 12.5%).
The Affinity Laws of centrifugal pumps or fans indicates the influence on volume capacity, head (pressure) and/or power consumption of a pump or fan due to
Pump Affinity Laws Volume Capacity The volume capacity of a centrifugal pump can be expressed like q1 / q2 = (n1 / n2)(d1 / d2) (1) where q = volume flow capacity (m3/s, gpm, cfm, ..) n = wheel velocity  revolution per minute  (rpm) d = wheel diameter Head or Pressure The head or pressure of a centrifugal pump can be expressed like dp1 / dp2 = (n1 / n2)2 (d1 / d2)2 (2) where dp = head or pressure (m, ft, Pa, psi, ..) Power The power consumption of a centrifugal pump can be expressed as P1 / P2 = (n1 / n2)3 (d1 / d2)3 (3) where P = power (W, bhp, ..) Changing the Wheel Velocity If the wheel diameter is constant  change in pump wheel velocity can simplify the affinity laws to Volume Capacity q1 / q2 = (n1 / n2) (1a) Head or Pressure dp1 / dp2 = (n1 / n2)2 (2a) Power P1 / P2 = (n1 / n2)3 (3a) Note! If the speed of a pump is increased with 10%
Pump Affinity Laws Calculator  Changing Wheel Velocity Replace the default values with the actual values. The calculator is generic and can be used with all common units as long as the use is consistent. Top of Form q1  volume capacity  (m3/s, gpm, cfm, ..) dp1  head or pressure (m, ft, Pa, psi, ..) P1  power (W, bhp) n1  initial wheel velocity (rpm) n2  final wheel velocity (rpm) Bottom of Form Changing the Impeller Diameter If wheel velocity is constant a change in impeller diameter can simplify the affinity laws to Volume Capacity q1 / q2 = d1 / d2 (1b) Head or Pressure dp1 / dp2 = (d1 / d2)2 (2b) Power P1 / P2 = (d1 / d2)3 (3b) Pump Affinity Laws Calculator  Changing Wheel Diameter Replace the default values with the actual values. The calculator is generic and can be used with all common units as long as the use is consistent. Top of Form q1  volume capacity  (m3/s, gpm, cfm, ..) dp1  head or pressure (m, ft, Pa, psi, ..) P1  power (W, bhp) d1  initial wheel diameter (m, in, ft ...) d2  final wheel diameter (m, in, ft ..) Bottom of Form Example  Pump Affinity Laws  Changing Pump Speed The pump speed is changed when the impeller size is constant. The initial flow is 100 gpm, the initial head is 100 ft, the initial power is 5 bhp, the initial speed is 1750 rpm and the final speed 3500 rpm. The final flow capacity can be calculated with (1a): q2 = q1 n2 / n1 = (100 gpm) (3500 rpm) / (1750 rpm) = 200 gpm The final head can be calculated with (2a): dp2 = dp1 (n2 / n1)2 = (100 ft) ((3500 rpm) / (1750 rpm))2 = 400 ft The final power consumption can be calculated with (3a): P2 = P1 (n2 / n1)3 = (5 bhp) ((3500 rpm) / (1750 rpm))3 = 40 bph Example  Pump Affinity Laws  Changing Impeller Diameter The diameter of the pump impeller is reduced when the pump speed is constant. The diameter is changed from 8 to 6 inches. The final flow capacity can be calculated with (1b): q2 = q1 (d2 / d1) = ( 100 gpm) ((¨6 in) / (8 in)) = 75 gpm The final head can be calculated with (2b): dp2 = dp1 (d2 / d1)2 = (100 ft) ((6 in) / ( 8 in))2 = 56.3 ft The final power consumption can be calculated with (3b): P2 = P1 (d2 / d1)3 = (5 bhp) ((6 in) / ( 8 in))3 = 2.1 bph
0 Comments
Leave a Reply. 
AuthorDan Berteletti is a Sustainability & Efficiency Innovator with a passion for frugal, simple, & smart living. Categories
All
