Pump and motor sizing (fluids.pump)

fluids.pump.VFD_efficiency(P, load=1)[source]

Returns the efficiency of a Variable Frequency Drive according to [R941952]. These values are generic, and not standardized as minimum values. Older VFDs often have much worse performance.

Parameters:

P : float

Power, [W]

load : float, optional

Fraction of motor’s rated electrical capacity being used

Returns:

efficiency : float

VFD efficiency, [-]

Notes

The use of a VFD does change the characteristics of a pump curve’s efficiency, but this has yet to be quantified. The effect is small. This value should be multiplied by the product of the pump and motor efficiency to determine the overall efficiency.

Efficiency table is in units of hp, so a conversion is performed internally. If load not specified, assumed 1 - where maximum efficiency occurs. Table extends down to 3 hp and up to 400 hp; values outside these limits are rounded to the nearest known value. Values between standardized sizes are interpolated linearly. Load values extend down to 0.016.

The table used is for Pulse Width Modulation (PWM) VFDs.

References

[R941952](1, 2) GoHz.com. Variable Frequency Drive Efficiency. http://www.variablefrequencydrive.org/vfd-efficiency

Examples

>>> VFD_efficiency(10*hp)
0.96
>>> VFD_efficiency(100*hp, load=0.2)
0.92
fluids.pump.CSA_motor_efficiency(P, closed=False, poles=2, high_efficiency=False)[source]

Returns the efficiency of a NEMA motor according to [R942953]. These values are standards, but are only for full-load operation.

Parameters:

P : float

Power, [W]

closed : bool, optional

Whether or not the motor is enclosed

poles : int, optional

The number of poles of the motor

high_efficiency : bool, optional

Whether or not to look up the high-efficiency value

Returns:

efficiency : float

Guaranteed full-load motor efficiency, [-]

Notes

Criteria for being required to meet the high-efficiency standard is:

  • Designed for continuous operation
  • Operates by three-phase induction
  • Is a squirrel-cage or cage design
  • Is NEMA type A, B, or C with T or U frame; or IEC design N or H
  • Is designed for single-speed operation
  • Has a nominal voltage of less than 600 V AC
  • Has a nominal frequency of 60 Hz or 50/60 Hz
  • Has 2, 4, or 6 pole construction
  • Is either open or closed

Pretty much every motor is required to meet the low-standard efficiency table, however.

Several low-efficiency standard high power values were added to allow for easy programming; values are the last listed efficiency in the table.

References

[R942953](1, 2) Natural Resources Canada. Electric Motors (1 to 500 HP/0.746 to 375 kW). As modified 2015-12-17. https://www.nrcan.gc.ca/energy/regulations-codes-standards/products/6885

Examples

>>> CSA_motor_efficiency(100*hp)
0.93
>>> CSA_motor_efficiency(100*hp, closed=True, poles=6, high_efficiency=True)
0.95
fluids.pump.motor_efficiency_underloaded(P, load=0.5)[source]

Returns the efficiency of a motor operating under its design power according to [R943954].These values are generic; manufacturers usually list 4 points on their product information, but full-scale data is hard to find and not regulated.

Parameters:

P : float

Power, [W]

load : float, optional

Fraction of motor’s rated electrical capacity being used

Returns:

efficiency : float

Motor efficiency, [-]

Notes

If the efficiency returned by this function is unattractive, use a VFD. The curves used here are polynomial fits to [R943954]‘s graph, and curves were available for the following motor power ranges: 0-1 hp, 1.5-5 hp, 10 hp, 15-25 hp, 30-60 hp, 75-100 hp If above the upper limit of one range, the next value is returned.

References

[R943954](1, 2, 3) Washington State Energy Office. Energy-Efficient Electric Motor Selection Handbook. 1993.

Examples

>>> motor_efficiency_underloaded(1*hp)
0.8705179600980149
>>> motor_efficiency_underloaded(10.1*hp,  .1)
0.6728425932357025
fluids.pump.Corripio_pump_efficiency(Q)[source]

Estimates pump efficiency using the method in Corripio (1982) as shown in [R944955] and originally in [R945955]. Estimation only

\[\eta_P = -0.316 + 0.24015\ln(Q) - 0.01199\ln(Q)^2\]
Parameters:

Q : float

Volumetric flow rate, [m^3/s]

Returns:

efficiency : float

Pump efficiency, [-]

Notes

For Centrifugal pumps only. Range is 50 to 5000 GPM, but input variable is in metric. Values above this range and below this range will go negative, although small deviations are acceptable. Example 16.5 in [R944955].

References

[R944955](1, 2, 3) Seider, Warren D., J. D. Seader, and Daniel R. Lewin. Product and Process Design Principles: Synthesis, Analysis, and Evaluation. 2 edition. New York: Wiley, 2003.
[R945955](1, 2) Corripio, A.B., K.S. Chrien, and L.B. Evans, “Estimate Costs of Centrifugal Pumps and Electric Motors,” Chem. Eng., 89, 115-118, February 22 (1982).

Examples

>>> Corripio_pump_efficiency(461./15850.323)
0.7058888670951621
fluids.pump.Corripio_motor_efficiency(P)[source]

Estimates motor efficiency using the method in Corripio (1982) as shown in [R946957] and originally in [R947957]. Estimation only.

\[\eta_M = 0.8 + 0.0319\ln(P_B) - 0.00182\ln(P_B)^2\]
Parameters:

P : float

Power, [W]

Returns:

efficiency : float

Motor efficiency, [-]

Notes

Example 16.5 in [R946957].

References

[R946957](1, 2, 3) Seider, Warren D., J. D. Seader, and Daniel R. Lewin. Product and Process Design Principles: Synthesis, Analysis, and Evaluation. 2 edition. New York: Wiley, 2003.
[R947957](1, 2) Corripio, A.B., K.S. Chrien, and L.B. Evans, “Estimate Costs of Centrifugal Pumps and Electric Motors,” Chem. Eng., 89, 115-118, February 22 (1982).

Examples

>>> Corripio_motor_efficiency(137*745.7)
0.9128920875679222
fluids.pump.specific_speed(Q, H, n=3600.0)[source]

Returns the specific speed of a pump operating at a specified Q, H, and n.

\[n_S = \frac{n\sqrt{Q}}{H^{0.75}}\]
Parameters:

Q : float

Flow rate, [m^3/s]

H : float

Head generated by the pump, [m]

n : float, optional

Speed of pump [rpm]

Returns:

nS : float

Specific Speed, [rpm*m^0.75/s^0.5]

Notes

Defined at the BEP, with maximum fitting diameter impeller, at a given rotational speed.

References

[R948959](1, 2) HI 1.3 Rotodynamic Centrifugal Pumps for Design and Applications

Examples

Example from [R948959].

>>> specific_speed(0.0402, 100, 3550)
22.50823182748925
fluids.pump.specific_diameter(Q, H, D)[source]

Returns the specific diameter of a pump operating at a specified Q, H, and D.

\[D_s = \frac{DH^{1/4}}{\sqrt{Q}}\]
Parameters:

Q : float

Flow rate, [m^3/s]

H : float

Head generated by the pump, [m]

D : float

Pump impeller diameter [m]

Returns:

Ds : float

Specific diameter, [m^0.25/s^0.5]

Notes

Used in certain pump sizing calculations.

References

[R949960]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> specific_diameter(Q=0.1, H=10., D=0.1)
0.5623413251903491
fluids.pump.speed_synchronous(f, poles=2, phase=3)[source]

Returns the synchronous speed of a synchronous motor according to [R950961].

\[N_s = \frac{120 f \cdot\text{phase}}{\text{poles}}\]
Parameters:

f : float

Line frequency, [Hz]

poles : int, optional

The number of poles of the motor

phase : int, optional

Line AC phase

Returns:

Ns : float

Speed of synchronous motor, [rpm]

Notes

Synchronous motors have no slip. Large synchronous motors are not self-starting.

References

[R950961](1, 2) All About Circuits. Synchronous Motors. Chapter 13 - AC Motors http://www.allaboutcircuits.com/textbook/alternating-current/chpt-13/synchronous-motors/

Examples

>>> speed_synchronous(50, poles=12)
1500.0
>>> speed_synchronous(60, phase=1)
3600.0
fluids.pump.nema_sizes = [186.42496789556753, 248.5666238607567, 372.84993579113507, 559.2749036867026, 745.6998715822701, 1118.5498073734052, 1491.3997431645403, 2237.0996147468104, 2982.7994863290805, 3728.4993579113507, 4101.349293702486, 5592.749036867026, 7456.998715822701, 11185.498073734052, 14913.997431645403, 18642.496789556753, 22370.996147468104, 29827.994863290805, 37284.99357911351, 44741.99229493621, 55927.49036867026, 74569.98715822701, 93212.48394778377, 111854.98073734052, 130497.47752689727, 149139.97431645403, 186424.96789556753, 223709.96147468104, 260994.95505379455, 298279.94863290805, 335564.94221202156, 372849.93579113507]

list: all NEMA motor sizes in increasing order, in Watts.

fluids.pump.nema_sizes_hp = [0.25, 0.3333333333333333, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 5.5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500]

list: all NEMA motor sizes in increasing order, in horsepower.

fluids.pump.motor_round_size(P)[source]

Rounds up the power for a motor to the nearest NEMA standard power. The returned power is always larger or equal to the input power.

Parameters:

P : float

Power, [W]

Returns:

P_actual : float

Actual power, equal to or larger than input [W]

Notes

An exception is raised if the power required is larger than any of the NEMA sizes. Larger motors are available, but are unstandardized.

References

[R951962]Natural Resources Canada. Electric Motors (1 to 500 HP/0.746 to 375 kW). As modified 2015-12-17. https://www.nrcan.gc.ca/energy/regulations-codes-standards/products/6885

Examples

>>> motor_round_size(1E5)
111854.98073734052
fluids.pump.current_ideal(P, V, phase=3, PF=1)[source]

Returns the current drawn by a motor of power P operating at voltage V, with line AC of phase phase and power factor PF according to [R952963].

Single-phase power:

\[I = \frac{P}{V \cdot \text{PF}}\]

3-phase power:

\[I = \frac{P}{V \cdot \text{PF} \sqrt{3}}\]
Parameters:

P : float

Power, [W]

V : float

Voltage, [V]

phase : int, optional

Line AC phase, either 1 or 3

PF : float, optional

Power factor of motor

Returns:

I : float

Power drawn by motor, [A]

Notes

Does not include power used by the motor’s fan, or startor, or internal losses. These are all significant.

References

[R952963](1, 2) Electrical Construction, and Maintenance. “Calculating Single- and 3-Phase Parameters.” April 1, 2008. http://ecmweb.com/basics/calculating-single-and-3-phase-parameters.

Examples

>>> current_ideal(V=120, P=1E4, PF=1, phase=1)
83.33333333333333