Cubic feet per hour to Cubic Millimeters per second conversion

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

Sure, let's walk through the conversion process from cubic feet per hour (ft³/hr) to cubic millimeters per second (mm³/s).

1. Convert Hours to Seconds:

   • There are 3600 seconds in one hour (60 seconds/minute × 60 minutes/hour).

2. Convert Cubic Feet to Cubic Millimeters:

   • One foot is equivalent to 304.8 millimeters.
   • To convert cubic feet to cubic millimeters, we need to cube the conversion factor: $1 \text{ ft} = 304.8 \text{ mm} \implies 1 \text{ ft}^3 = (304.8 \text{ mm})^3$
   • Calculating this, $1 \text{ ft}^3 = 304.8^3 \text{ mm}^3 \approx 2.831684659 \times 10^7 \text{ mm}^3$

3. Combine the Conversions:

   • We need the volume flow rate in cubic feet per hour converted to cubic millimeters per second.

So, combining these steps:

$1 \text{ ft}^3/\text{hr} = \left(2.831684659 \times 10^7 \text{ mm}^3\right) / 3600 \text{ s}$

Performing the division:

$1 \text{ ft}^3/\text{hr} \approx 7865.79 \text{ mm}^3/\text{s}$

Therefore, 1 cubic foot per hour is approximately 7865.79 cubic millimeters per second.

Real-World Examples:

Now let's use this conversion factor for some other quantities.

1. Residential Water Use:

   • A typical household faucet might flow at a rate of about 2.2 gallons per minute. $1 \text{ gallon} \approx 0.133681 \text{ ft}^3$
   • So, $2.2 \text{ gallons/minute} \approx 2.2 \times 0.133681 \text{ ft}^3/\text{minute} \approx 0.294098 \text{ ft}^3/\text{minute} \approx 17.65 \text{ ft}^3/\text{hr}$
   • Converting this to mm³/s: $17.65 \text{ ft}^3/\text{hr} \approx 17.65 \times 7865.79 \text{ mm}^3/\text{s} \approx 138764 \text{ mm}^3/\text{s}$

2. Industrial Applications:

   • An industrial pump might flow at a rate of 500 ft³/hr.
   • Converting to mm³/s: $500 \text{ ft}^3/\text{hr} \approx 500 \times 7865.79 \text{ mm}^3/\text{s} \approx 3932895 \text{ mm}^3/\text{s}$

3. Natural Gas Flow:

   • A large industrial gas line might transport natural gas at 10,000 ft³/hr.
   • Converting to mm³/s: $10000 \text{ ft}^3/\text{hr} \approx 10000 \times 7865.79 \text{ mm}^3/\text{s} \approx 78657900 \text{ mm}^3/\text{s}$

These conversions help in understanding and comparing various flow rates across different contexts, translating to a more intuitive grasp of the numbers involved.