Pump Affinity Laws

[B]The Affinity Laws[/B] of centrifugal pumps or fans indicates the influence on volume capacity, head (pressure) and/or power consumption of a pump or fan due to
[INDENT]
[LIST][*]change in [B]speed[/B] of wheel - revolutions per minute (rpm) [*]geometrically similarity - change in [B]impeller diameter[/B] [/LIST][/INDENT]
Note that the affinity laws for fans are not identical with pumps.
[B]Pump Affinity Laws[/B]

[B]Volume Capacity[/B]

[I]The volume capacity of a centrifugal pump can be expressed like[/I][INDENT] [I]q[SUB]1[/SUB] / q[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB][/I][I])(d[SUB]1[/SUB] / d[SUB]2[/SUB]) (1)[/I]
[I]where[/I]
[I]q[/I] [I]= volume flow capacity (m[SUP]3[/SUP]/s, gpm, cfm, ..)[/I]
[I][I]n[/I] = wheel velocity - revolution per minute - (rpm)[/I]
[I]d = wheel diameter[/I][/INDENT]
[B]Head or Pressure[/B]

The head or pressure of a centrifugal pump can be expressed like[INDENT] [I]dp[SUB]1[/SUB] / dp[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB])[/I][SUP][I]2[/I][/SUP] [I](d[SUB]1[/SUB] / d[SUB]2[/SUB])[SUP]2[/SUP] (2)[/I]
[I]where[/I]
[I][I]dp[/I] = head or pressure (m, ft, Pa, psi, ..)[/I][/INDENT]
[B]Power[/B]

The power consumption of a centrifugal pump can be expressed as[INDENT] [I]P[SUB]1[/SUB] / P[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB])[SUP]3[/SUP][/I] [I](d[SUB]1[/SUB] / d[SUB]2[/SUB])[SUP]3[/SUP] (3)[/I]
[I]where[/I]
[I]P[/I] [I]= power (W, bhp, ..)[/I][/INDENT]
[B][B]Changing the Wheel Velocity[/B][/B]


[CENTER][img]http://www.egpet.net/vb/images/imported/2012/01/2.png[/img][/CENTER]
If the [B]wheel diameter is constant[/B] - change in pump wheel velocity can simplify the affinity laws to
[B]Volume Capacity[/B]

[INDENT] [I]q[SUB]1[/SUB] / q[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB]) (1a)[/I][/INDENT]
[B]Head or Pressure[/B]

[INDENT] [I]dp[SUB]1[/SUB] / dp[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB])[/I][SUP][I]2 [/I][/SUP] [I](2a)[/I][/INDENT]
[B]Power[/B]

[INDENT] [I]P[SUB]1[/SUB] / P[SUB]2[/SUB] = (n[SUB]1[/SUB] / n[SUB]2[/SUB])[SUP]3[/SUP][/I] [I](3a)[/I][/INDENT]
[CENTER][img]http://www.egpet.net/vb/images/imported/2012/01/3.png[/img][/CENTER]
[B]Note![/B] If the speed of a pump is increased with [I]10%[/I]

[LIST][*]the volume flow increases with [I]10%[/I] [*]the head increases with [I]21%[/I] [*]the power increases with [I]33 %[/I] [/LIST]
If we want to increase the volume flow capacity of an existing system with [I]10%[/I] we have to increase the power supply with [I]33%[/I].
[B]Pump Affinity Laws Calculator - Changing Wheel Velocity[/B]

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.


[B][B]Changing the Impeller Diameter[/B][/B]

If wheel velocity is constant [B]a change in impeller diameter[/B] can simplify the affinity laws to
[B]Volume Capacity[/B]

[INDENT] [I]q[SUB]1[/SUB] / q[SUB]2[/SUB] =[/I] [I]d[SUB]1[/SUB] / d[SUB]2[/SUB] (1b)[/I][/INDENT]
[B]Head or Pressure[/B]

[INDENT] [I]dp[SUB]1[/SUB] / dp[SUB]2[/SUB] =[/I] [I](d[SUB]1[/SUB] / d[SUB]2[/SUB])[SUP]2[/SUP] (2b)[/I][/INDENT]
[B]Power[/B]

[INDENT] [I]P[SUB]1[/SUB] / P[SUB]2[/SUB] =[/I] [I](d[SUB]1[/SUB] / d[SUB]2[/SUB])[SUP]3[/SUP] (3b)[/I][/INDENT]
[CENTER][img]http://www.egpet.net/vb/images/imported/2012/01/4.png[/img][/CENTER]
[B]Pump Affinity Laws Calculator - Changing Wheel Diameter[/B]

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. [INDENT] [I]q[SUB]1[/SUB] - volume capacity - (m[SUP]3[/SUP]/s, gpm, cfm, ..)[/I]
[I]dp[SUB]1[/SUB] - head or pressure (m, ft, Pa, psi, ..)[/I]
[I]P[SUB]1[/SUB] - power (W, bhp)[/I]
[I]d[SUB]1[/SUB] - initial wheel diameter (m, in, ft ...)[/I]
[I]d[SUB]2[/SUB] - final wheel diameter (m, in, ft ..)[/I][/INDENT]
[B]Example - Pump Affinity Laws - Changing Pump Speed[/B]

The pump speed is changed when the impeller size is constant. The initial flow is [I]100 gpm[/I], the initial head is [I]100 ft[/I], the initial power is [I]5 bhp[/I], the initial speed is [I]1750 rpm[/I] and the final speed [I]3500 rpm[/I].
The final flow capacity can be calculated with (1a):[INDENT] [I]q[SUB]2[/SUB] = q[SUB]1[/SUB] n[SUB]2[/SUB] / n[SUB]1[/SUB] [/I]
[I] =[/I] [I](100 gpm) (3500 rpm) / (1750 rpm) [/I]
[I] = [U]200[/U] gpm[/I][/INDENT]
The final head can be calculated with (2a):[INDENT] [I]dp[SUB]2[/SUB] = dp[SUB]1[/SUB] (n[SUB]2[/SUB] / n[SUB]1[/SUB])[/I][SUP][I]2[/I][/SUP]
[I]= (100 ft) ((3500 rpm) / (1750 rpm))[SUP]2[/SUP] [/I]
[I] = [U]400[/U] ft[/I][/INDENT]
The final power consumption can be calculated with (3a):[INDENT] [I]P[SUB]2[/SUB] = P[SUB]1[/SUB] (n[SUB]2[/SUB] / n[SUB]1[/SUB])[SUP]3[/SUP][/I]
[I]= (5 bhp) ((3500 rpm) / (1750 rpm))[SUP]3[/SUP] [/I]
[I] = [U]40[/U] bph[/I][/INDENT]
[B]Example - Pump Affinity Laws - Changing Impeller Diameter[/B]

The diameter of the pump impeller is reduced when the pump speed is constant. The diameter is changed from [I]8 to 6 inches[/I].
The final flow capacity can be calculated with (1b):[INDENT] [I]q[SUB]2[/SUB] = q[SUB]1[/SUB] (d[SUB]2[/SUB] / d[/I][SUB][I]1[/I][/SUB][I]) [/I]
[I] = ( 100 gpm) ((¨6 in) / (8 in)) [/I]
[I] = [U]75[/U] gpm[/I][/INDENT]
The final head can be calculated with (2b):[INDENT] [I]dp[SUB]2[/SUB] = dp[SUB]1[/SUB][/I] [I](d[/I][I][SUB]2[/SUB] / d[/I][SUB][I]1[/I][/SUB][I])[SUP]2[/SUP] [/I]
[I] = (100 ft) ((6 in) / ( 8 in))[SUP]2[/SUP] [/I]
[I] = [U]56.3[/U] ft[/I][/INDENT]
The final power consumption can be calculated with (3b):[INDENT] [I]P[SUB]2[/SUB] = P[SUB]1[/SUB] (d[SUB]2[/SUB] / d[/I][SUB][I]1[/I][/SUB][I])[SUP]3[/SUP] [/I]
[I] = (5 bhp) ((6 in) / ( 8 in))[SUP]3[/SUP] [/I]
[I] = [U]2.1[/U] bph[/I]
[/INDENT]