Pump Formulas — Imperial and SI Units
Pressure to Head
Imperial Units
SI Units
H = head, ft
P = pressure, psi
SG = specific gravity
H = head, m
P = pressure, bar
SG = specific gravity
Mass Flow to Volumetric Flow
Imperial Units
SI Units
Q = flow, gpm
ṁ = mass flow, lbm/h
SG = specific gravity
3
ρ = fluid density, lbm/ft
Q = flow, m /h
ṁ = mass flow, kg/h
3
ρ = fluid density, kg/m
3
Net Positive Suction Head
In terms of head
Imperial Units
SI Units
NPSH = net positive suction head at reference point
(usually center line of the impeller), ft
Ha = absolute pressure of the suction vessel, ft
Hvpa = fluid vapor pressure at pumping temperature, ft
Hst = static head to suction reference point (usually center
line of the impeller), ft
Hfs = suction line losses, ft
NPSH = net positive suction head at reference point
(usually center line of the impeller), m
Ha = absolute pressure of the suction vessel, m
Hvpa = fluid vapor pressure at pumping temperature, m
Hst = static head to suction reference line (usually center
point of the impeller), m
Hfs = suction line losses, m
1
In terms of pressure and head
Imperial Units
SI Units
NPSH = net positive suction head at reference point
(usually center line of the impeller), ft
Pa = absolute pressure of the suction vessel, psia
Pvpa = fluid vapor pressure at pumping temperature, psia
Hst = static head at reference point (usually center line of
the impeller), ft
Hfs = suction line losses, ft
SG = specific gravity
NPSH = net positive suction head at reference point
(usually center line of the impeller), m
Pa = absolute pressure of the suction vessel, kPa
Pvpa = fluid vapor pressure at pumping temperature, kPa
absolute
Hst = static head to suction reference line (usually center
point of the impeller), m
Hfs = suction line losses, m
3
ρ = fluid density, kg/m
2
g = gravitational constant, 9.81 m/s
Pump Head
Imperial Units
SI Units
H = pump head, ft
Hf = friction loss, ft
PS = suction pressure, psia
Pd = discharge pressure, psia
SG = specific gravity
Vs = suction velocity, ft/s
Vd = discharge velocity, ft/s
Zs = suction height from reference, ft
Zd = discharge head from reference, ft
2
g = gravitational constant, 32.2 ft/s
H = pump head, m
Hf = friction loss, m
PS = suction pressure, bar
Pd = discharge pressure, bar
SG = specific gravity
Vs = suction velocity, m/s
Vd = discharge velocity, m/s
Zs = suction height from reference, m
Zd = Discharge head from reference, m
2
g = gravitational constant, 9.81 m/s
2
Pump Power
Imperial Units
SI Units
P = power, horse power
H = head, ft
Q = flow, gpm
SG = specific gravity
= pump efficiency, decimal
P = power, kW
H = head, m
3
Q = flow, m /hr
SG = specific gravity
= pump efficiency, decimal
Pump Torque
Imperial Units
SI Units
τ = torque, ft-lbf
P = pump power, hp
N = pump speed, rpm
τ = torque, N-m
P = pump power, kW
N = pump speed, rpm
Temperature Rise
Imperial Units
SI Units
ΔT = temperature rise, °F
H = total head, ft
η = pump efficiency, decimal
U = fluid specific heat, BTU/(lbm-°F)
ΔT = temperature rise, °C or °K
H = total head, m
η = pump efficiency, decimal
U = fluid specific heat, kJ/(kg-°K) or kJ/(kg-°C)
3
Fluid Velocity
Imperial Units
SI Units
V = velocity, ft/s
Q = flow, gpm
d = pipe inside diameter, in
V = velocity, m/s
3
Q = flow, m /h
d = pipe inside diameter, mm
Velocity Head
Imperial Units
SI Units
Hv = velocity head, ft of liquid
V = fluid velocity, ft/s
2
g = gravitational constant, 32.2 ft/s
Q = flow, gpm
d = pipe inside diameter, in
Hv = velocity head, m
V = fluid velocity, m/s
2
g = gravitational constant, 9.81 m/s
3
Q = flow, m /h
d = pipe inside diameter, mm
Specific Speed at BEP
Imperial Units
SI Units
Ns = specific speed
N = pump speed, rpm
Q = flow, gpm
H = head, ft
Values are taken at best efficiency point (BEP)
Pump flow is taken at the largest impeller diameter
For double suction impellers pump flow is divided by two
Ns = specific speed
N = pump speed, rpm
3
Q = flow, m /h
H = head, m
Values are taken at best efficiency point (BEP)
Pump flow is taken at the largest impeller diameter
For double suction impellers pump flow is divided by two
4
Suction Specific Speed at BEP
Imperial Units
SI Units
Ns = specific speed
N = pump speed, rpm
Q = flow, gpm
NPSH = net positive suction head, ft
Values are taken at best efficiency point (BEP)
Pump flow is taken at the largest impeller diameter
For double suction impellers pump flow is divided by two
Ns = specific speed
N = pump speed, rpm
3
Q = flow, m /h
NPSH = net positive suction head, m
Values are taken at best efficiency point (BEP)
Pump flow is taken at the largest impeller diameter
For double suction impellers pump flow is divided by two
5
Other Pump Formulas
Affinity Laws
Changes in Diameter
Changes in Speed
D = diameter, in or mm
3
Q = flow, gpm or m /h
H = head, ft or m
P = power, hp or kW
Q = flow, gpm or m /h
H = head, ft or m
P = power, hp or kW
N = speed, rpm
3
Bernoulli’s Equation
g = gravitational constant
L = energy losses
PS = suction pressure
Pd = discharge pressure
Vs = suction velocity
Vd = discharge velocity
W = work by the pump
Zs = suction height from reference
Zd = discharge head from reference
ρ = fluid density
γ = fluid specific weight = g*ρ
6
Tables
Conversion Factors
Imperial Conversions
From
To
barrel (oil) – bbl
gallon – US gal
barrel (oil) – bbl
cubic meter – m3
British thermal unit – Btu
Joule – J
British thermal unit per hour – Btu/h
Watt – W
cubic feet – ft3
cubic meter – m3
3
cubic feet per minute – ft /min or cfm
cubic meters per hour – m3/h
feet – ft
meter – m
foot pounds force – ft-lbf
Joule – J
gallon (US) – US gal
cubic meter – m3
gallon (US) – US gal
liter – l
gallon (US) – US gal
gallon (Imperial) – Imp gal
gallon (US) per minute – gpm
cubic meter per hour – m3/h
gallon (US) per minute – gpm
barrel (oil) per day – b/d
horsepower – hp
kilowatt – kW
horsepower hour – hp-h
kilojoule – kJ
horsepower hour – hp-h
British thermal unit per hour – Btu
inch – in
millimeter – mm
inch of mercury at 0°F – inHg
kilopascal – kPa
inch of water at 68°F – inH2O
kilopascal – kPa
mile
kilometer – km
pound force – lbf
Newton – N
pound mass – lbm
kilogram – kg
pound force per square inch – psi
kilopascal – kPa
pound force per square inch – psi
bar
ton (long)
ton (short)
ton (short)
kilogram – kg
yard – yd
meter – m
Note
1. Conversions less than four significant digits are exact.
Multiply By1
42
0.159 0
1 055
0.293 1
0.028 32
1.699
0.304 8
1.356
0.003 785
3.785
0.832 7
0.227 1
34.28
0.745 7
2 684
2 545
25.4
3.386
0.248 7
1.609
4.448
0.453 6
6.895
0.068 95
1.12
907.2
0.914 4
7
SI Conversions
From
bar
bar
cubic meter – m3
cubic meter – m3
cubic meter per hour – m3/hr
cubic meter per hour – m3/hr
kilograms – kg
kilogram per square centimeter – kg/cm2
kilogram per square centimeter – kg/cm2
kilometer – km
kilopascal – kPa
kilowatt – kW
kilowatt hour – kW-h
kilowatt hours – kW-h
meter – m
Newton – N
To
kilopascal – kPa
pounds force per square inch – psi
gallons – US gal
cubic feet – ft3
gallons per minute – gpm
barrel per day – b/d
pounds mass – lbm
Bar
pounds force per square inch – psi
mile
pounds force per square inch – psi
horsepower – hp
British thermal units per hour – Btu
Kilojoule – kJ
feet – ft
pound force – lbf
Multiply By
100
14.50
264.2
35.31
4.403
337.3
2.205
0.980 7
14.22
0.621 4
0.145 0
1.341
3.413
3 600
3.281
0.224 8
SI Prefixes
Power of Ten
1012
109
106
103
10
10-1
10-2
10-3
10-6
10-9
10-12
Name
tera
giga
mega
kilo
deca
deci
centi
milli
micro
nano
pico
Symbol
T
G
M
k
da
d
c
m
μ
n
p
8
Symbols and Nomenclature
Symbol
A
D, d
g
H
h
ṁ
N
Ns
Nss
P
P
Q
s
U
V
W
Z
NPSH
SG
η
ρ
τ
ΔT
γ
Definition
Area
Diameter
Gravitational constant
Head
Time
Mass flow rate
Speed
Specific speed
Suction specific speed
Power
Pressure
Flow
Time
Specific heat
Velocity
Work
Elevation
Net positive suction head
Specific gravity
Efficiency
Density
Torque
Temperature change
Specific weight
Imperial Units
ft2
inches
32.2 ft/s2
ft
hour
lbm/h
rpm
Dimensionless
Dimensionless
horsepower
psi
gpm
seconds
btu/lbm-°F
ft/s
ft
ft
ft
Dimensionless
Dimensionless
lbm/ft3
ft-lbf
°F
lbf/ft3
SI Units
m2
mm
9.81 m/s2
m
hour
kg/h
rpm
Dimensionless
Dimensionless
kW
kPa or bar
m3/h
seconds
kJ/kg-°C
m/s
m
m
m
Dimensionless
Dimensionless
Kg/m3
N-m
°C
kN/m3
9