Cubic inches per minute to Cubic meters per second conversion

How to convert cubic inches per minute to cubic meters per second?

To convert cubic inches per minute (in³/min) to cubic meters per second (m³/s), you need to follow these steps:

1. Convert cubic inches to cubic meters: There are $0.000016387064$ cubic meters in one cubic inch (since $1 \text{ in} = 0.0254 \text{ m}$, so $1 \text{ in}^3 = (0.0254 \text{ m})^3$).

2. Convert minutes to seconds: There are 60 seconds in a minute.

The formula for conversion is:

$1 \, \text{in}^3/\text{min} \times \frac{0.000016387064 \, \text{m}^3}{1 \, \text{in}^3} \times \frac{1 \, \text{min}}{60 \, \text{s}} = \frac{0.000016387064 \, \text{m}^3}{60 \, \text{s}}$

Now, compute the value:

$1 \, \text{in}^3/\text{min} = \frac{0.000016387064}{60} \, \text{m}^3/\text{s} \approx 2.7311773 \times 10^{-7} \, \text{m}^3/\text{s}$

So, 1 cubic inch per minute is approximately $2.7311773 \times 10^{-7} \, \text{m}^3/\text{s}$.

Real World Examples

1. Air Compressor: Many household air compressors have an output of around 2 to 6 cubic inches per minute (approximately $5.4623546 \times 10^{-7} \text{m}^3/\text{s}$ to $1.6387064 \times 10^{-6} \text{m}^3/\text{s}$).

2. Pneumatic Tools: A small pneumatic nail gun might use air at a rate of about 50 cubic inches per minute (approximately $1.36558865 \times 10^{-5} \, \text{m}^3/\text{s}$).

3. HVAC System: Many HVAC units have air flow rates measured in cubic feet per minute (CFM), but this can be converted to cubic inches per minute. For example, a small office space might require an HVAC system to provide airflow of around 200 CFM, equivalent to $3456000 \text{ in}^3/\text{min}$ (since $1 \text{ ft}^3 = 12^3 \text{ in}^3 = 1728 \text{ in}^3$).

$200 \, \text{CFM} \times 1728 \, \text{in}^3/\text{ft}^3 = 345600 \, \text{in}^3/\text{min}$

Converted to cubic meters per second, this is approximately $9.439512 \times 10^{-3} \, \text{m}^3/\text{s}$.

Understanding these conversions helps in various engineering and practical applications where different units of measurement are used.