Cubic feet per minute to Cubic Millimeters per second conversion

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

To convert cubic feet per minute (CFM) to cubic millimeters per second (mm³/s), you need to follow these steps:

1. Understand the units involved:

   • 1 cubic foot (ft³) is equal to $1,728$ cubic inches (in³).
   • 1 cubic inch (in³) is equal to $16,387.064$ cubic millimeters (mm³).
   • There are $60$ seconds in a minute.

2. Conversion:

   • First, convert cubic feet to cubic millimeters.
   • Then, convert minutes to seconds.

Step-by-Step Conversion

1. Convert cubic feet to cubic inches:

$1 \, \text{ft}³ = 1,728 \, \text{in}³$

2. Convert cubic inches to cubic millimeters:

$1,728 \, \text{in}³ \times 16,387.064 \, \text{mm}³/\text{in}³ = 28,316,846.59 \, \text{mm}³$

3. Convert minutes to seconds:

Since we are given 1 ft³/min, we need to convert flow rate per minute to flow rate per second.

$\frac{28,316,846.59 \, \text{mm}³}{60 \, \text{seconds}} = 471,947.44 \, \text{mm}³/\text{s}$

Therefore, 1 cubic foot per minute is approximately $471,947.44$ cubic millimeters per second.

Real World Examples

Different Quantities of Cubic Feet per Minute:

1. Residential Kitchen Range Hood:

   • Suppose a kitchen exhaust fan has a flow rate of $300 \, \text{CFM}$.
   • Conversion: $300 \, \text{ft}³/\text{min} \times 471,947.44 \, \text{mm}³/\text{s}$ $= 141,584,233.2 \, \text{mm}³/\text{s}$

2. HVAC System in Large Buildings:

   • Let's take an industrial HVAC system with a flow rate of $10,000 \, \text{CFM}$.
   • Conversion: $10,000 \, \text{ft}³/\text{min} \times 471,947.44 \, \text{mm}³/\text{s}$ $= 4,719,474,400 \, \text{mm}³/\text{s}$

3. Computer Cooling Fan:

   • A high-performance computer cooling fan may have a flow rate of $50 \, \text{CFM}$.
   • Conversion: $50 \, \text{ft}³/\text{min} \times 471,947.44 \, \text{mm}³/\text{s}$ $= 23,597,372 \, \text{mm}³/\text{s}$

These examples demonstrate how you can convert cubic feet per minute to cubic millimeters per second for various applications to understand the scale and impact of different flow rates in different contexts.