Cubic inches per minute to Cubic meters per hour conversion

How to convert cubic inches per minute to cubic meters per hour?

To convert cubic inches per minute (in³/min) to cubic meters per hour (m³/h), you need to account for both the volume and time unit conversions. Here's the step-by-step process:

Conversion Factors

1. Volume:

   • 1 cubic inch (in³) = 1.63871 × 10⁻⁵ cubic meters (m³)

2. Time:

   • 1 minute = 1/60 hours

Conversion Formula

To convert any value from cubic inches per minute to cubic meters per hour, you can use the following formula:

$\text{Cubic meters per hour (m³/h)} = \text{Cubic inches per minute (in³/min)} \times \frac{1.63871 \times 10^{-5} \text{ m³/in³}}{1/60 \text{ hours/min}}$

Example Calculation

Let's convert 1 in³/min to m³/h:

$\text{m³/h} = 1 \text{ in³/min} \times \frac{1.63871 \times 10^{-5} \text{ m³/in³}}{1/60 \text{ hours/min}}$

$\text{m³/h} = 1 \times 1.63871 \times 10^{-5} \times 60$

$\text{m³/h} = 9.83226 \times 10^{-4}$

So, 1 cubic inch per minute is approximately $9.83226 \times 10^{-4}$ cubic meters per hour.

Real-World Examples

5 in³/min:

$\text{m³/h} = 5 \times 9.83226 \times 10^{-4}$ $\text{m³/h} = 4.91613 \times 10^{-3}$

50 in³/min:

$\text{m³/h} = 50 \times 9.83226 \times 10^{-4}$ $\text{m³/h} = 4.91613 \times 10^{-2}$

100 in³/min:

$\text{m³/h} = 100 \times 9.83226 \times 10^{-4}$ $\text{m³/h} = 9.83226 \times 10^{-2}$

1000 in³/min:

$\text{m³/h} = 1000 \times 9.83226 \times 10^{-4}$ $\text{m³/h} = 9.83226 \times 10^{-1}$

Practical Application

These conversions can be useful in various fields:

1. Engineering: For designing systems that require specific flow rates of fluids, such as cooling systems or hydraulic systems.
2. Manufacturing: Understanding volumetric flow in processes like casting or injection molding.
3. Environmental Science: Measuring rates of pollutant flow or water discharge.

By understanding these conversions, you can better interpret and manage systems that involve fluid dynamics, ensuring they operate efficiently and effectively.