Cubic inches per hour to Cubic yards per minute conversion

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

To convert from cubic inches per hour to cubic yards per minute, we'll need to follow these steps:

1. Convert cubic inches to cubic yards.
2. Convert hours to minutes.

Step-by-Step Conversion

Unit Conversions

1. Cubic inches to cubic yards:

   The conversion factor between cubic inches and cubic yards is: $1 \text{ cubic yard} = 27 \text{ cubic feet} \times 1,728 \text{ cubic inches per cubic foot} = 46,656 \text{ cubic inches}$ Therefore: $1 \text{ cubic inch} = \frac{1}{46,656} \text{ cubic yard}$

2. Hours to minutes:

   The conversion factor between hours and minutes is: $1 \text{ hour} = 60 \text{ minutes}$

Conversion Process for 1 Cubic Inch per Hour

1. Convert cubic inches to cubic yards: $1 \text{ cubic inch per hour} = \frac{1}{46,656} \text{ cubic yards per hour}$

2. Now, convert cubic yards per hour to cubic yards per minute by dividing by the number of minutes in an hour: $\frac{1 \text{ cubic inch per hour}}{46,656} \text{ cubic yards per hour} \times \frac{1}{60} \text{ hour per minute} = \frac{1}{46,656 \times 60} \text{ cubic yards per minute} = \frac{1}{2,799,360} \text{ cubic yards per minute}$

So: $1 \text{ Cubic inch per hour} = \frac{1}{2,799,360} \text{ Cubic yards per minute}$

Real World Examples

Let’s convert a few more common flow rates in cubic inches per hour to cubic yards per minute for context:

Example 1: 10,000 Cubic Inches per Hour

1. Convert cubic inches to cubic yards per hour: $10,000 \text{ cubic inches per hour} = \frac{10,000}{46,656} \text{ cubic yards per hour} \approx 0.214 \text{ cubic yards per hour}$

2. Convert cubic yards per hour to cubic yards per minute: $0.214 \text{ cubic yards per hour} \div 60 \approx 0.00357 \text{ cubic yards per minute}$

Example 2: 1,000 Cubic Inches per Hour

1. Convert cubic inches to cubic yards per hour: $1,000 \text{ cubic inches per hour} = \frac{1,000}{46,656} \text{ cubic yards per hour} \approx 0.0214 \text{ cubic yards per hour}$

2. Convert cubic yards per hour to cubic yards per minute: $0.0214 \text{ cubic yards per hour} \div 60 \approx 0.000357 \text{ cubic yards per minute}$

Example 3: 100 Cubic Inches per Hour

1. Convert cubic inches to cubic yards per hour: $100 \text{ cubic inches per hour} = \frac{100}{46,656} \text{ cubic yards per hour} \approx 0.00214 \text{ cubic yards per hour}$

2. Convert cubic yards per hour to cubic yards per minute: $0.00214 \text{ cubic yards per hour} \div 60 \approx 0.0000357 \text{ cubic yards per minute}$

These examples illustrate how small the flow rates can be when converting from cubic inches per hour to cubic yards per minute, due to the significant difference in the size of the units.