Cups per second to Cubic yards per minute conversion

How to convert cups per second to cubic yards per minute?

To convert from cups per second to cubic yards per minute, you'll need to follow these steps:

1. Convert cups to cubic yards.
2. Convert seconds to minutes.

First, we need the conversion factors:

• There are 16 cups in a gallon.
• There are 231 cubic inches in a gallon.
• A cubic yard is 27 cubic feet.
• There are 12 inches in a foot, so 1 cubic yard is $27 \times 12^3 = 46,656$ cubic inches.
• There are 60 seconds in a minute.

Step 1: Convert cups to cubic inches.

$1 \, \text{cup} = \frac{231 \, \text{cubic inches}}{16}$

$1 \, \text{cup} = 14.4375 \, \text{cubic inches}$

Step 2: Convert cubic inches to cubic yards.

$1 \, \text{cubic inch} = \frac{1}{46,656} \, \text{cubic yards}$

$1 \, \text{cup} = 14.4375 \times \frac{1}{46,656} = 0.000309 \, \text{cubic yards}$

Step 3: Convert cups per second to cubic yards per minute.

Since there are 60 seconds in a minute:

$1 \, \text{cup/second} = 0.000309 \, \text{cubic yards/second} \times 60 = 0.01854 \, \text{cubic yards/minute}$

Therefore, 1 cup per second is equivalent to 0.01854 cubic yards per minute.

Real-world Examples for Other Quantities of Cups per Second:

1. Water Flow in a Small Garden Hose:

   • A garden hose delivering water at 2 cups per second.
   • $2 \, \text{cups/second} = 2 \times 0.01854 = 0.03708 \, \text{cubic yards/minute}$ (or approximately 1.034 gallons per second).

2. Beverage Dispenser:

   • A dispenser serving soda at 0.5 cups per second.
   • $0.5 \, \text{cups/second} = 0.5 \times 0.01854 = 0.00927 \, \text{cubic yards/minute}$ (or approximately 0.129 gallons per second).

3. Pumping Rate from Water Pump:

   • A small water pump with an output of 10 cups per second.
   • $10 \, \text{cups/second} = 10 \times 0.01854 = 0.1854 \, \text{cubic yards/minute}$ (or approximately 8.03 gallons per second).

Using these steps and conversions, you can calculate volume flow rates in different units for various applications by adjusting the quantities of cups per second.