Cubic inches per second to Cubic yards per second conversion

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

To convert from cubic inches per second to cubic yards per second, you need to know the relationship between these two units of volume. There are 46,656 cubic inches in one cubic yard.

Here's a step-by-step method to convert cubic inches per second to cubic yards per second:

1. Understand the relationship:

   • 1 cubic yard (yd³) = 46,656 cubic inches (in³).

2. Set up the conversion factor:

   • Conversion factor: $\text{1 yd³} = 46,656 \text{ in³}$.

3. Convert 1 cubic inch per second to cubic yards per second: $1 \text{ cubic inch/second} \times \left( \frac{1 \text{ yd³}}{46,656 \text{ in³}} \right) = \frac{1}{46,656} \text{ cubic yards/second}$ $\approx 2.14 \times 10^{-5} \text{ cubic yards/second}$

Thus, 1 cubic inch per second is approximately $2.14 \times 10^{-5}$ cubic yards per second.

Real-World Examples

1. Garden Hose:

   • A typical garden hose might deliver water at a rate of about 10 to 15 gallons per minute.
   • Since 1 gallon is approximately 231 cubic inches, at 10 gallons per minute: $10 \text{ gal/min} \times 231 \text{ in³/gal} = 2,310 \text{ in³/min}$ Converting to per second: $2,310 \text{ in³/min} \div 60 \approx 38.5 \text{ in³/s}$

2. 1 Cubic Yard per Hour:

   • Let's say a machine processes material at the rate of 1 cubic yard per hour.
   • Since there are 46,656 cubic inches in a cubic yard and 3600 seconds in an hour: $1 \text{ yd³/hour} \times \left( \frac{46,656 \text{ in³}}{3600 \text{ seconds}} \right) \approx 12.96 \text{ in³/s}$

3. Swimming Pool:

   • Consider a pool pump that filters 10,000 gallons per hour.
   • Converting gallons to cubic inches (1 gallon ≈ 231 in³): $10,000 \text{ gal/hour} \times 231 \text{ in³/gal} = 2,310,000 \text{ in³/hour}$ Converting to per second: $2,310,000 \text{ in³/hour} \div 3600 \approx 641.7 \text{ in³/s}$

These examples provide a context for how cubic inches per second can be used in various real-world scenarios, illustrating the scale and practicality of the unit conversions.