Density Dependent Flow Rate Calculator
Flow 1
Flow Rate:*
Density:
Temperature:
Density of Water (kg/m³): 998
Flow 2
Flow Rate Units:*
Density:
Temperature:
Density of Water (kg/m³): 998
Result (lb/hr / PPH): Result (GPM): Result (kg/sec): Result (gram/min): Result (lb/sec): Result (lb/min): Result (kg/min): Result (kg/hr): Result (gram/sec): Result (ton/hr metric): Result (in³/sec): Result (ft³/sec): Result (m³/sec): Result (mm³/sec): Result (L/min):  

*Mixed Mass and Volume Flow Rate Units*

Mass is always conserved, Mass In = Mass Out

Volume is NOT always conserved, Volume In ≠ Volume Out

Specific Gravity is a temperature dependent unit

Specific Gravity is a Contentious Unit

Water Densities per this page.

Multi Flow Density Dependent Flow Rate Calculator
Flow 1 + Flow 2 = Flow 3
Flow 1
Flow Rate:*
Density:
Temperature:
Density of Water (kg/m³): 998
Flow 2
Flow Rate:*
Density:
Temperature:
Density of Water (kg/m³): 998
Flow 3
Flow Rate Units:*
Density:
Temperature:
Density of Water (kg/m³): 998
Result (lb/hr / PPH): Result (GPM): Result (kg/sec): Result (gram/min): Result (lb/sec): Result (lb/min): Result (kg/min): Result (kg/hr): Result (gram/sec): Result (ton/hr metric): Result (in³/sec): Result (ft³/sec): Result (m³/sec): Result (mm³/sec): Result (L/min):  

*Mixed Mass and Volume Flow Rate Units*

Mass is always conserved, Mass In = Mass Out

Volume is NOT always conserved, Volume In ≠ Volume Out

Specific Gravity is a temperature dependent unit

Specific Gravity is a Contentious Unit

Water Densities per this page.

Also See:  

PPH to GPM Calculator

Also See:  

Water Density Compensated Universal PPH to GPM Calculator
Reference Guide: Density-Dependent Flow Rates
01

PPH vs. GPM: Mass Flow and Volume Flow

Fuel flow is measured two ways. Mass flow, in pounds per hour (PPH), is what an engine burns, because the energy in fuel comes from its mass. Volume flow, in gallons per minute (GPM), is what pumps, valves and many flow meters handle.

Density links the two. It is the weight of one gallon, about 6.7 lb for jet fuel. Density changes with temperature: warm fuel is lighter, so the same PPH takes more GPM.

Mass flow = density × volume flow\[ \dot m = \rho\,Q \]
A fuel line with a mass flow meter reading PPH and a volume flow meter reading GPM. A one-gallon block of fuel weighs about 6.7 pounds; dividing PPH by 60 times the pounds per gallon gives GPM.
Two Meters, One Flow
The same flow reads in pounds or in gallons. The fuel's density converts one into the other.
02

Every Unit Cancels

Written out with every unit, the conversion is a chain of factors that each equal one. Every unit cancels except gallons per minute:

PPH → GPM, unit by unit\[ \text{GPM}\ \frac{\text{gal}}{\text{min}} = \text{PPH}\ \frac{\cancel{\text{lb}}}{\cancel{\text{hr}}} \times \frac{1\ \cancel{\text{hr}}}{60\ \text{min}} \times \frac{27{,}679.90471\ \cancel{\text{kg}/\text{m}^3}}{1\ \cancel{\text{lb}}/\cancel{\text{in}^3}} \times \frac{1}{\text{SG}} \times \frac{1}{\rho_{\text{water}}\ \cancel{\text{kg}/\text{m}^3}} \times \frac{1\ \text{gal}}{231\ \cancel{\text{in}^3}} \]
GPM → PPH, unit by unit\[ \text{PPH}\ \frac{\text{lb}}{\text{hr}} = \text{GPM}\ \frac{\cancel{\text{gal}}}{\cancel{\text{min}}} \times \frac{60\ \cancel{\text{min}}}{1\ \text{hr}} \times \text{SG} \times \rho_{\text{water}}\ \cancel{\text{kg}/\text{m}^3} \times \frac{1\ \text{lb}/\cancel{\text{in}^3}}{27{,}679.90471\ \cancel{\text{kg}/\text{m}^3}} \times \frac{231\ \cancel{\text{in}^3}}{1\ \cancel{\text{gal}}} \]
Why the Numbers Are Exact

None of the constants is a rounded measurement. The pound and the inch are defined exactly in SI units (1 lb = 0.45359237 kg and 1 in = 0.0254 m), the US gallon is defined as exactly 231 in³, and an hour is 60 minutes. That makes 27,679.90471 kg/m³ exactly one pound per cubic inch:

One pound per cubic inch\[ 1\ \frac{\text{lb}}{\text{in}^3} = \frac{0.45359237\ \text{kg}}{(0.0254\ \text{m})^3} = 27{,}679.90471\ \frac{\text{kg}}{\text{m}^3} \]

The only inputs that carry real uncertainty are the specific gravity and the water density it is referenced to.

03

Converting PPH ↔ GPM

With the density in pounds per gallon, the factor of 60 converts hours to minutes:

PPH → GPM\[ \text{GPM} = \frac{\text{PPH}}{60 \times \rho_{\text{lb/gal}}} \]
GPM → PPH\[ \text{PPH} = \text{GPM} \times 60 \times \rho_{\text{lb/gal}} \]
Density from specific gravity\[ \rho_{\text{lb/gal}} = \text{SG} \times \rho_{\text{water}} \times \frac{231}{27{,}679.9} \]
Example

10,000 PPH of jet fuel with SG = 0.80, referenced to water at 60 °F (999.0 kg/m³):

\[ \begin{gathered} \rho = 0.80 \times 999.0 \times \frac{231}{27{,}679.9} = 6.670\ \text{lb/gal} \\ \text{GPM} = \frac{10{,}000}{60 \times 6.670} = 24.99 \end{gathered} \]
Rule of thumb: for jet fuel near 6.7 lb/gal, 1 GPM is about 400 PPH. Check the density at the actual fuel temperature for anything more than a rough estimate.
04

Density & Specific Gravity Conversions

Specific gravity (SG) is the fluid's density divided by the density of water. It has no units, which makes it easy to quote, but it is only exact once you know which water it is compared to.

Specific gravity\[ \text{SG} = \frac{\rho_{\text{fluid}}}{\rho_{\text{water}}} \qquad \rho_{\text{fluid}} = \text{SG} \times \rho_{\text{water}} \]

Water is 999.0 kg/m³ at 60 °F and 1,000.0 kg/m³ at 4 °C. Fuel specifications usually quote SG at 60 °F. The water-density-compensated calculators compare against water at the fluid's own temperature instead. See why specific gravity is a contentious unit.

kg/m³ → lb/gal and lb/in³\[ \begin{gathered} \rho_{\text{lb/gal}} = \rho_{\text{kg/m}^3} \times \frac{231}{27{,}679.9} = \frac{\rho_{\text{kg/m}^3}}{119.83} \\ \rho_{\text{lb/in}^3} = \frac{\rho_{\text{kg/m}^3}}{27{,}679.9} \end{gathered} \]
UnitEquals
1 lb/in³27,679.9 kg/m³
1 lb/gal (US)119.83 kg/m³
1 lb/ft³16.018 kg/m³
1 US gallon231 in³ = 3.7854 L
05

Mass Is Conserved, Volume Is Not

When fuel warms up or cools down, its mass flow stays the same but its volume flow changes, because the density changes.

Same mass, different density\[ \rho_1\,Q_1 = \rho_2\,Q_2 \quad\Rightarrow\quad Q_2 = Q_1\,\frac{\rho_1}{\rho_2} \]
Example

Fuel at 810 kg/m³ is heated until its density falls to 780 kg/m³. The PPH does not change, but the volume flow rises by \(810/780 = 1.038\), so a pump or meter downstream sees 3.8% more GPM.

Mixing Streams

When two streams of different density join, mass adds but volume does not have to:

Mixing two flows\[ \dot m_3 = \dot m_1 + \dot m_2 \qquad Q_3 = \frac{\dot m_3}{\rho_3} \]
Volumes do not simply add. Add the mass flows, then divide by the density of the mixture. Adding GPM directly is only right when both streams have the same density.

Cite This Work