Cubic inches per hour to Cubic yards per second conversion

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

To convert from cubic inches per hour (in³/hr) to cubic yards per second (yd³/s), you need to follow these steps:

1. Convert cubic inches to cubic yards:

   • There are 36 inches in a yard, meaning there are $36^3 = 46,656$ cubic inches in a cubic yard.

2. Convert hours to seconds:

   • There are 3600 seconds in an hour.

So, to convert cubic inches per hour to cubic yards per second, you use the following relationship:

$1 \ \text{in}^3/\text{hr} = \frac{1 \ \text{in}^3}{46,656 \ \text{yd}^3} \times \frac{1 \ \text{hr}}{3,600 \ \text{s}}$

Simplifying that gives:

$1 \ \text{in}^3/\text{hr} = \frac{1}{46,656 \times 3,600} \ \text{yd}^3/\text{s}$

$1 \ \text{in}^3/\text{hr} = \frac{1}{167,961,600} \ \text{yd}^3/\text{s} \approx 5.96 \times 10^{-9} \ \text{yd}^3/\text{s}$

Real-world Examples:

1. Small Pumping System for an Aquarium:

   • Suppose you have an aquarium pump that moves water at a rate of 10,000 cubic inches per hour. $10,000 \ \text{in}^3/\text{hr} \approx 10,000 \times 5.96 \times 10^{-9} \ \text{yd}^3/\text{s}$ $\approx 5.96 \times 10^{-5} \ \text{yd}^3/\text{s}$

2. Car Engine Displacement:

   • If an engine displaces air at a rate of 600,000 cubic inches per hour. $600,000 \ \text{in}^3/\text{hr} \approx 600,000 \times 5.96 \times 10^{-9} \ \text{yd}^3/\text{s}$ $\approx 3.58 \times 10^{-3} \ \text{yd}^3/\text{s}$

3. Water Flow in a Small Irrigation System:

   • Imagine an irrigation system that delivers water at 1,500 cubic inches per hour. $1,500 \ \text{in}^3/\text{hr} \approx 1,500 \times 5.96 \times 10^{-9} \ \text{yd}^3/\text{s}$ $\approx 8.94 \times 10^{-6} \ \text{yd}^3/\text{s}$

By understanding these conversions and real-world examples, you can relate cubic inches per hour to cubic yards per second and apply this to various practical situations.