Cubic feet per hour to Teaspoons per second conversion

How to convert cubic feet per hour to teaspoons per second?

To convert cubic feet per hour ($\text{ft}^3/\text{hr}$) to teaspoons per second (tsp/s), you need to use a series of conversions to bridge the gap between these two units.

Here's a step-by-step guide to the conversion:

1. Convert cubic feet to cubic inches: 1 cubic foot (ft³) is equivalent to 1728 cubic inches (in³) because there are 12 inches in a foot (12 inches)^3 = 1728 cubic inches.

   $1 \, \text{ft}^3 = 1728 \, \text{in}^3$

2. Convert cubic inches to teaspoons: 1 cubic inch is equivalent to approximately 3.32468 teaspoons.

   $1 \, \text{in}^3 \approx 3.32468 \, \text{tsp}$

3. Convert hours to seconds: 1 hour is equal to 3600 seconds.

   $1 \, \text{hr} = 3600 \, \text{s}$

4. Combine the conversions: To find the equivalent rate in teaspoons per second:

   $1 \, \text{ft}^3/\text{hr} \times \frac{1728 \, \text{in}^3}{1 \, \text{ft}^3} \times \frac{3.32468 \, \text{tsp}}{1 \, \text{in}^3} \times \frac{1 \, \text{hr}}{3600 \, \text{s}}$

   Simplify the units (ft³ and in³ cancel out) to get:

   $1 \, \text{ft}^3/\text{hr} = \frac{1728 \times 3.32468 \, \text{tsp}}{3600 \, \text{s}}$

   Calculate the numerical value:

   $1 \, \text{ft}^3/\text{hr} = \frac{5748.6 \, \text{tsp}}{3600 \, \text{s}}$

   $1 \, \text{ft}^3/\text{hr} \approx 1.5963 \, \text{tsp/s}$

So, 1 cubic foot per hour is approximately 1.5963 teaspoons per second.

Real-world Examples with Different Quantities of Cubic Feet per Hour

1. Kitchen Faucet Flow Rate: A typical kitchen faucet might have a flow rate of about 1500 cubic feet per hour.

   Convert this to teaspoons per second:

   $1500 \, \text{ft}^3/\text{hr} \times 1.5963 \, \text{tsp/s per ft}^3/\text{hr} = 2394.45 \, \text{tsp/s}$

2. Industrial Fan Flow Rate: An industrial fan could have a flow rate of around 500 cubic feet per hour.

   Convert this to teaspoons per second:

   $500 \, \text{ft}^3/\text{hr} \times 1.5963 \, \text{tsp/s per ft}^3/\text{hr} = 798.15 \, \text{tsp/s}$

3. Human Breathing Rate: The average human breathes at a rate of about 0.2 cubic feet per hour while at rest.

   Convert this to teaspoons per second:

   $0.2 \, \text{ft}^3/\text{hr} \times 1.5963 \, \text{tsp/s per ft}^3/\text{hr} = 0.31926 \, \text{tsp/s}$

These examples illustrate how the flow rate can significantly differ depending on the context and utility of the measurement.