Cubic inches per second to Cubic feet per hour conversion

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

To convert cubic inches per second (in³/s) to cubic feet per hour (ft³/hr), you need to follow a couple of conversion steps.

1. Convert cubic inches to cubic feet:

   • There are 12 inches in a foot, so there are $12 \times 12 \times 12 = 1,728$ cubic inches in a cubic foot.
   • Therefore, $1 \text{ cubic inch} = \frac{1}{1,728} \text{ cubic feet}$

2. Convert seconds to hours:

   • There are 60 seconds in a minute and 60 minutes in an hour, so there are $60 \times 60 = 3,600$ seconds in an hour.

So, the general formula to convert $x$ cubic inches per second (in³/s) to cubic feet per hour (ft³/hr) is: $x \text{ in³/s} \times \left(\frac{1 \text{ ft³}}{1,728 \text{ in³}}\right) \times 3,600 \text{ sec/hr} = x \times \frac{3,600}{1,728} \text{ ft³/hr}$

Simplify the fraction: $\frac{3,600}{1,728} = \frac{25}{12} \approx 2.0833$

Thus, $x \text{ in³/s} \approx x \times 2.0833 \text{ ft³/hr}$

For 1 in³/s: $1 \text{ in³/s} \times 2.0833 = 2.0833 \text{ ft³/hr}$

Real-World Examples:

1. Water Flow through a small pipe:

   • Suppose a small garden hose has a flow rate of 2 in³/s.
   • Converted to cubic feet per hour: $2 \text{ in³/s} \approx 2 \times 2.0833 = 4.167 \text{ ft³/hr}$

2. Airflow in a duct:

   • A residential air conditioning unit may circulate air at approximately 50 in³/s.
   • Converted to cubic feet per hour: $50 \text{ in³/s} \approx 50 \times 2.0833 = 104.165 \text{ ft³/hr}$

3. Industrial Fluid Transfer:

   • An industrial pump might have a capacity of 500 in³/s.
   • Converted to cubic feet per hour: $500 \text{ in³/s} \approx 500 \times 2.0833 = 1,041.65 \text{ ft³/hr}$

These examples illustrate how the conversion applies to various practical scenarios from small-scale household applications to large-scale industrial operations.