Pump and motor sizing (fluids.pump)¶
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fluids.pump.
VFD_efficiency
(P, load=1)[source]¶ Returns the efficiency of a Variable Frequency Drive according to [R624]. 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
[R624] (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
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fluids.pump.
CSA_motor_efficiency
(P, closed=False, poles=2, high_efficiency=False)[source]¶ Returns the efficiency of a NEMA motor according to [R625]. 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
[R625] (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
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fluids.pump.
motor_efficiency_underloaded
(P, load=0.5)[source]¶ Returns the efficiency of a motor operating under its design power according to [R626].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 [R626]’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
[R626] (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
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fluids.pump.
Corripio_pump_efficiency
(Q)[source]¶ Estimates pump efficiency using the method in Corripio (1982) as shown in [R627] and originally in [R628]. 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 [R627].
References
[R627] (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. [R628] (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
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fluids.pump.
Corripio_motor_efficiency
(P)[source]¶ Estimates motor efficiency using the method in Corripio (1982) as shown in [R629] and originally in [R630]. 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 [R629].
References
[R629] (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. [R630] (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
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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
[R631] (1, 2) HI 1.3 Rotodynamic Centrifugal Pumps for Design and Applications Examples
Example from [R631].
>>> specific_speed(0.0402, 100, 3550) 22.50823182748925
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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
[R632] 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
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fluids.pump.
speed_synchronous
(f, poles=2, phase=3)[source]¶ Returns the synchronous speed of a synchronous motor according to [R633].
\[N_s = \frac{120 f \cdot\text{phase}}{\text{poles}}\]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
[R633] (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
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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.
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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.
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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
[R634] 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
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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 [R635].
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
[R635] (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
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fluids.pump.
liquid_jet_pump
(rhop, rhos, Km=0.15, Kd=0.1, Ks=0.1, Kp=0.0, d_nozzle=None, d_mixing=None, d_diffuser=None, Qp=None, Qs=None, P1=None, P2=None, P5=None, nozzle_retracted=True)[source]¶ Calculate the remaining variable in a liquid jet pump, using a model presented in [R636] as well as [R637], [R638], and [R639].
\[ \begin{align}\begin{aligned}N = \frac{2R + \frac{2 C M^2 R^2}{1-R} - R^2 (1+CM) (1+M) (1 + K_m + K_d + \alpha^2) - \frac{CM^2R^2}{(1-R)^2} (1+K_s)} {(1+K_p) - 2R - \frac{2CM^2R^2}{1-R} + R^2(1+CM)(1+M)(1+K_m + K_d + \alpha^2) + (1-j)\left(\frac{CM^2R^2}{({1-R})^2} \right)(1+K_s)}\\\text{Pressure ratio} = N = \frac{P_5 - P_2}{P_1 - P_5}\\\text{Volume flow ratio} = M = \frac{Q_s}{Q_p}\\\text{Jet pump efficiency} = \eta = M\cdot N = \frac{Q_s(P_5-P_2)}{Q_p(P_1 - P_5)}\\R = \frac{A_n}{A_m}\\C = \frac{\rho_s}{\rho_p}\end{aligned}\end{align} \]Parameters: rhop : float
The density of the primary (motive) fluid, [kg/m^3]
rhos : float
The density of the secondary fluid (drawn from the vacuum chamber), [kg/m^3]
Km : float, optional
The mixing chamber loss coefficient, [-]
Kd : float, optional
The diffuser loss coefficient, [-]
Ks : float, optional
The secondary inlet loss coefficient, [-]
Kp : float, optional
The primary nozzle loss coefficient, [-]
d_nozzle : float, optional
The inside diameter of the primary fluid’s nozle, [m]
d_mixing : float, optional
The diameter of the mixing chamber, [m]
d_diffuser : float, optional
The diameter of the diffuser at its exit, [m]
Qp : float, optional
The volumetric flow rate of the primary fluid, [m^3/s]
Qs : float, optional
The volumetric flow rate of the secondary fluid, [m^3/s]
P1 : float, optional
The pressure of the primary fluid entering its nozzle, [Pa]
P2 : float, optional
The pressure of the secondary fluid at the entry of the ejector, [Pa]
P5 : float, optional
The pressure at the exit of the diffuser, [Pa]
nozzle_retracted : bool, optional
Whether or not the primary nozzle’s exit is before the mixing chamber, or somewhat inside it, [-]
Returns: solution : dict
Dictionary of calculated parameters, [-]
Notes
The assumptions of the model are:
- The flows are one dimensional except in the mixing chamber.
- The mixing chamber has constant cross-sectional area.
- The mixing happens entirely in the mixing chamber, prior to entry into the diffuser.
- The primary nozzle is in a straight line with the middle of the mixing chamber.
- Both fluids are incompressible, and have no excess volume on mixing.
- Primary and secondary flows both enter the mixing throat with their own uniform velocity distribution; the mixed stream leaves with a uniform velocity profile.
- If the secondary fluid is a gas, it undergoes isothermal compression in the throat and diffuser.
- If the secondary fluid is a gas or contains a bubbly gas, it is homogeneously distributed in a continuous liquid phase.
- Heat transfer between the fluids is negligible - there is no change in density due to temperature changes
- The change in the solubility of a disolved gas, if there is one, is negigibly changed by temperature or pressure changes.
References
[R636] (1, 2) Karassik, Igor J., Joseph P. Messina, Paul Cooper, and Charles C. Heald. Pump Handbook. 4th edition. New York: McGraw-Hill Education, 2007. [R637] (1, 2) Winoto S. H., Li H., and Shah D. A. “Efficiency of Jet Pumps.” Journal of Hydraulic Engineering 126, no. 2 (February 1, 2000): 150-56. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:2(150). [R638] (1, 2) Elmore, Emily, Khalid Al-Mutairi, Bilal Hussain, and A. Sherif El-Gizawy. “Development of Analytical Model for Predicting Dual-Phase Ejector Performance,” November 11, 2016, V007T09A013. [R639] (1, 2) Ejectors and Jet Pumps. Design and Performance for Incompressible Liquid Flow. 85032. ESDU International PLC, 1985. Examples
>>> pprint(liquid_jet_pump(rhop=998., rhos=1098., Km=.186, Kd=0.12, Ks=0.11, ... Kp=0.04, d_nozzle=0.0223, d_mixing=0.045, Qs=0.01, Qp=.01, P2=133600, ... P5=200E3, nozzle_retracted=False)) {'M': 1.0, 'N': 0.2938665390183575, 'P1': 425952.91121542786, 'P2': 133600, 'P5': 200000.0, 'Qp': 0.01, 'Qs': 0.01, 'R': 0.24557530864197535, 'alpha': 1e-06, 'd_diffuser': 45.0, 'd_mixing': 0.045, 'd_nozzle': 0.0223, 'efficiency': 0.2938665390183575}