Cubic inches per hour to Cubic feet per second conversion

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

To convert cubic inches per hour (in³/hr) to cubic feet per second (ft³/s), you need to understand the relationship between these units. There are 12 inches in a foot, so there are $12 \times 12 \times 12 = 1728$ cubic inches in a cubic foot. Additionally, there are 3600 seconds in an hour.

Here’s the step-by-step conversion process:

1. Convert cubic inches to cubic feet: $1 \text{ in}^3 = \frac{1}{1728} \text{ ft}^3$

2. Convert hours to seconds: $1 \text{ hr} = 3600 \text{ s}$

Given 1 in³/hr:

3. Calculate cubic feet per second: $1 \text{ in}^3/\text{hr} \times \frac{1 \text{ ft}^3}{1728 \text{ in}^3} \times \frac{1 \text{ hr}}{3600 \text{ s}} = \frac{1}{1728 \times 3600} \text{ ft}^3/\text{s}$

4. Simplify the expression: $\frac{1}{1728 \times 3600} = \frac{1}{6220800} \approx 1.606 \times 10^{-7} \text{ ft}^3/\text{s}$

Thus, 1 in³/hr equals approximately 1.606 × 10⁻⁷ ft³/s.

Real World Examples of Other Quantities of Cubic Inches per Hour

1. Household Aquarium Pump: A small household aquarium pump might circulate water at a rate of 10,000 in³/hr. $10,000 \text{ in}^3/\text{hr} \times \frac{1 \text{ ft}^3}{1728 \text{ in}^3} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 0.0058 \text{ ft}^3/\text{s}$

2. HVAC System: A medium-sized HVAC system might move air at 1,000,000 in³/hr. $1,000,000 \text{ in}^3/\text{hr} \times \frac{1 \text{ ft}^3}{1728 \text{ in}^3} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 0.1606 \text{ ft}^3/\text{s}$

3. Industrial Pump System: An industrial pump system may handle 10,000,000 in³/hr. $10,000,000 \text{ in}^3/\text{hr} \times \frac{1 \text{ ft}^3}{1728 \text{ in}^3} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 1.606 \text{ ft}^3/\text{s}$

These real world examples illustrate how flow rates in cubic inches per hour can vary significantly based on the application, and how such values can be converted to cubic feet per second for practical analysis.