Fluid Ounces per minute to Cubic feet per second conversion

How to convert fluid ounces per minute to cubic feet per second?

To convert from fluid ounces per minute (fl oz/min) to cubic feet per second (ft³/s), you need to understand the relationship between these units.

First, let's break down the units involved:

1. There are 128 fluid ounces in a gallon (US).
2. There are 7.48052 gallons in a cubic foot.
3. There are 60 seconds in a minute.

Start by converting fluid ounces to cubic feet:

1. Convert fluid ounces to gallons: $1 \text{ fl oz} = \frac{1}{128} \text{ gallons}$

2. Convert gallons to cubic feet: $1 \text{ gallon} = \frac{1}{7.48052} \text{ ft}³$

So, combining the two conversions: $1 \text{ fl oz} = \frac{1}{128 \times 7.48052} \text{ ft}³$

Now we have: $1 \text{ fl oz} = \frac{1}{957.50656} \text{ ft}³$

Now, convert fluid ounces per minute to cubic feet per second: $1 \text{ fl oz/min} = \frac{1}{957.50656} \text{ ft}³/\text{min}$

Next, convert minutes to seconds (since there are 60 seconds in a minute): $1 \text{ fl oz/min} = \frac{1}{957.50656 \times 60} \text{ ft}³/\text{s}$

$1 \text{ fl oz/min} \approx 1.74296 \times 10^{-5} \text{ ft}³/\text{s}$

So, the conversion factor is approximately: $1 \text{ fl oz/min} \approx 1.74296 \times 10^{-5} \text{ ft}³/\text{s}$

Real-World Examples:

1. Beverage Dispenser:

   • A standard soda dispenser might pour at a rate of 10 fl oz/min.
   • In cubic feet per second: $10 \text{ fl oz/min} = 10 \times 1.74296 \times 10^{-5} \text{ ft}³/\text{s} = 1.74296 \times 10^{-4} \text{ ft}³/\text{s}$

2. Small Pump:

   • A small aquarium pump might operate at 50 fl oz/min.
   • In cubic feet per second: $50 \text{ fl oz/min} = 50 \times 1.74296 \times 10^{-5} \text{ ft}³/\text{s} = 8.7148 \times 10^{-4} \text{ ft}³/\text{s}$

3. Household Faucet:

   • A household faucet might flow at 100 fl oz/min.
   • In cubic feet per second: $100 \text{ fl oz/min} = 100 \times 1.74296 \times 10^{-5} \text{ ft}³/\text{s} = 1.74296 \times 10^{-3} \text{ ft}³/\text{s}$

Understanding these conversions can help in applications like designing plumbing systems, calibrating pumps, or comparing different fluid flow rates in various engineering contexts.