Cubic Millimeters per second to Gallons per minute conversion

How to convert cubic millimeters per second to gallons per minute?

To convert cubic millimeters per second (mm³/s) to gallons per minute (GPM), you need to go through several steps involving unit conversions. Here’s how you can approach this:

1. Convert cubic millimeters to cubic meters:

   • There are $1,000,000,000$ cubic millimeters (mm³) in a cubic meter (m³).
   • Therefore, $1 \text{ mm³/s} = 1 \times 10^{-9} \text{ m³/s}$.

2. Convert cubic meters per second to cubic meters per minute:

   • There are 60 seconds in a minute.
   • So, $1 \text{ m³/s} = 60 \text{ m³/min}$.
   • Therefore, $1 \times 10^{-9} \text{ m³/s} = 1 \times 10^{-9} \text{ m³/s} \times 60 = 6 \times 10^{-8} \text{ m³/min}$.

3. Convert cubic meters to gallons:

   • 1 cubic meter is approximately 264.172 gallons.
   • So, to convert cubic meters per minute to gallons per minute: $6 \times 10^{-8} \text{ m³/min} \times 264.172 \text{ gal/m³} = 1.585032 \times 10^{-5} \text{ gal/min}$.

Thus, 1 cubic millimeter per second is approximately $1.585 \times 10^{-5}$ gallons per minute.

Real-World Examples for Other Quantities of Cubic Millimeters per Second:

1. 0.1 mm³/s (0.1 cubic millimeters per second):

   • Using the conversion factor above: $0.1 \text{ mm³/s} = 1.585 \times 10^{-6} \text{ gal/min}.$
   • Example in context: This flow rate might be found in precision dosing equipment used in chemical processes or medical infusions.

2. 100 mm³/s (100 cubic millimeters per second):

   • Using the conversion factor above: $100 \text{ mm³/s} = 1.585 \times 10^{-3} \text{ gal/min}.$
   • Example in context: Such a flow rate could be seen in laboratory experiments where moderate amounts of a fluid are required over time.

3. 10,000 mm³/s (10,000 cubic millimeters per second):

   • Using the conversion factor above: $10,000 \text{ mm³/s} = 0.1585 \text{ gal/min}.$
   • Example in context: This flow rate could be typical for a small pump system used in aquariums or small-scale water fountains.

4. 1,000,000 mm³/s (1,000,000 cubic millimeters per second):

   • Using the conversion factor above: $1,000,000 \text{ mm³/s} = 1.585 \text{ gal/min}.$
   • Example in context: This could represent the flow rate through domestic water supply lines, typically for uses like garden hoses and residential plumbing systems.

Summary

The conversion from cubic millimeters per second (mm³/s) to gallons per minute (GPM) is done through a series of conversions: mm³/s to m³/s to m³/min to GPM. Using these conversions can help contextualize various flow rates you might encounter in real-world applications.