Cubic inches per second to Cubic yards per hour conversion

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

To convert cubic inches per second to cubic yards per hour, you can follow these steps:

1. Convert cubic inches to cubic yards:

   • There are 12 inches in a foot, so there are $12 \times 12 \times 12 = 1728$ cubic inches in a cubic foot.
   • There are 3 feet in a yard, so there are $3 \times 3 \times 3 = 27$ cubic feet in a cubic yard.
   • Therefore, there are $1728 \times 27 = 46656$ cubic inches in a cubic yard.

2. Convert seconds to hours:

   • There are 60 seconds in a minute and 60 minutes in an hour.
   • So, there are $60 \times 60 = 3600$ seconds in an hour.

Given these conversions: 1 cubic inch per second = $\frac{1 \text{ cubic inch}}{1 \text{ second}}$

To find how many cubic yards per hour this corresponds to:

$1 \; \text{cubic inch/second} \times \frac{3600 \; \text{seconds}}{\text{hour}} \times \frac{1 \; \text{cubic yard}}{46656 \; \text{cubic inches}}$

Now, do the math:

$1 \; \text{cubic inch/second} = \frac{3600}{46656} \; \text{cubic yards/hour}$

$\frac{3600}{46656} = 0.07716$ (approximately)

Therefore:

$1 \; \text{cubic inch/second} \approx 0.07716 \; \text{cubic yards/hour}$

Real-world examples:

1. Water Flow in a Small Fountain:

   • A small fountain might pump water at a rate of about 10 cubic inches per second.
   • Converting this to cubic yards per hour: $10 \; \text{cubic inches/second} \approx 10 \times 0.07716 = 0.7716 \; \text{cubic yards/hour}$

2. Industrial Processes:

   • In some industrial processes, fluids may be pumped at a rate of 100 cubic inches per second.
   • Converting this: $100 \; \text{cubic inches/second} \approx 100 \times 0.07716 = 7.716 \; \text{cubic yards/hour}$

3. Large Water Pump System:

   • A more substantial pump, such as those used in municipal water systems or large-scale irrigation, could have a flow rate of 500 cubic inches per second.
   • Converting this: $500 \; \text{cubic inches/second} \approx 500 \times 0.07716 = 38.58 \; \text{cubic yards/hour}$