# Pump Calculations and Equations

Here's a list of some basic equations that are used in pump sizing. The primary question in choosing a pump is “What horsepower do I need?’

## Formulas For Reciprocating Pumps

##### I know what maximum PSI and maximum GPM I need. What size pump do I need?
Reciprocating Pump Formula:
Minimum Horsepower Required = Max GPM × Max PSI ÷ 1550
##### I have a pump with no tags or specifications on it. How do I find out what Gallons Per Minute (GPM) this pump is capable of?
(Plunger Radius × Plunger Radius × 3.142) = Sq. Inches of Circle
(Sq. Inches of Circle) × (Stroke Length) × (Number of Plungers) = Cubic Inches of Liquid Per Revolution
Cubic Inches of Liquid Per Revolution ÷ 231 = Gallons Per Revolution
(Gallons Per Revolution) × (Max RPM) = Gallons Per Minute

NOTE: Max RPM in the above equation varies according to type of pump, size of stroke, and other variables. Duplex pumps often run about 100 RPM Max. while triplex pumps will run somewhere between 100 RPM Max and 400 RPM Max.
##### I have a reciprocating pump and I know what my max rated rod load is (in foot pounds). I also know what PSI I need. What size plungers do I need?
Min. Plunger Size Needed = Square Root of (Rod Load Rating of Pump ÷ Max. PSI ÷ 3.142)

## Formulas For Centrifugal Pumps

##### I know what maximum PSI and maximum GPM I need. What size pump do I need?
Centrifugal Pump Formula:
Minimum Horsepower Required = ((Max GPM) × (Max PSI) ÷ 1710) ÷ (Efficiency in Percentage) × (specific gravity of material)
##### How do I calculate PSI (Pressure in Pounds Per Square Inch) or TDH (Total Dynamic Head)?
Assuming you have one measurement for your pump but not the other:
PSI = TDH ÷ 2.31
TDH = PSI × 2.31
##### How do I calculate Brake Horsepower Required for a centrifugal pump?
Brake Horsepower Required = GPM Required × (Total Dynamic Head) ÷ 3940 ÷ Efficiency

## General Equations

1 Barrel = 42 gallons

Gallons Per Minute = Barrels Per Day × .0292
GPM = BPD × .0292

Horsepower = Torque in Inch Pounds × (Revolutions Per Minute) ÷ 63,025
HP = ((Torque in Inch Pounds) × RPM) ÷ 63,025

1 US Liquid Gallon = 231 Cubic Inches
1 US Liquid Gallon = 231 Inches^3

1 US Liquid Gallon = 0.13368 Cubic Feet
1 US Liquid Gallon = 0.13368 Feet^3

1 US Liquid Gallon = 3.78541 Liters
1 Liter = 0.26417 US Liquid Gallons

1 Cubic Foot = 7.84 US Liquid Gallons
1 Foot^3 = 7.84 US Liquid Gallons

1 Cubic Foot = 28.31685 Liters
1 Foot^3 = 28.31685 Liters

Cubic Feet Per Day = Cubic Feet Per Minute × 1440
Feet^3 Per Day = (Feet^3 Per Minute) × 1440

Cubic Feet Per Minute = Cubic Feet Per Day ÷ 1440 Minutes Per Day
Feet^3 Per Minute = (Feet^3 Per Day) ÷ 1440 Minutes Per Day

## Chart of Relative Density / Specific Gravity for Common Liquids

Specific Gravity is used when sizing a centrifugal pump. Liquids with a specific gravity greater than 1.0 are heavier than water and conversely, liquids with a specific gravity lower than 1.0 are lighter weight than water and will generally float on water.

Material Degrees Celsius Degress Fahrenheit Specific Gravity
Alcohol, ethyl (ethanol) 25 77 0.787
Alcohol, methyl (methanol) 25 77 0.791
Alcohol, propyl 25 77 0.802
Butane, liquid 25 77 0.601
Crude oil, California 15.56 60 0.918
Crude oil, Mexico 15.56 60 0.976
Crude oil, Texas 15.56 60 0.876
Ethane -89 -128.2 0.572
Ethylene glycol 25 77 1.100
Gasoline, Natural 15.56 60 0.713
Gasoline, Vehicle 15.56 60 0.739
Kerosene 15.56 60 0.820
Methane -164 -263.2 0.466
Octane 25 77 0.701
Oxygen -183 -297.4 1.14
Propane -40 -40 0.585
Propane 25 77 0.495
Water, pure 4 39.2 1.0
Water, sea 25 77 1.025