Cubic meters per second to Cubic inches per hour conversion

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

To convert cubic meters per second (m³/s) to cubic inches per hour (in³/hr), you'll need to go through a step-by-step conversion process involving unit conversions for both volume and time.

Step-by-Step Conversion

1. Convert cubic meters to cubic inches:

   • 1 cubic meter (m³) is equal to $(100 \text{ cm})^3 = 1,000,000 \text{ cubic centimeters (cm³)}$.
   • 1 cubic centimeter (cm³) is equal to 0.0610237 cubic inches (in³).

   Hence, $1 \text{ cubic meter (m³)} = 1,000,000 \text{ cm³} \times 0.0610237 \text{ in³/cm³} = 61,023.7 \text{ in³}$.

2. Convert seconds to hours:

   • There are 3,600 seconds in an hour (60 seconds/minute * 60 minutes/hour).

3. Combine conversions:

   • If the flow rate is 1 cubic meter per second (m³/s), over the span of one hour: $(1 \text{ m³/s}) \times \left(61,023.7 \text{ in³/m³}\right) \times (3,600 \text{ s/hr}) \\ = 61,023.7 \text{ in³/s} \times 3,600 \text{ s/hr} \\ = 219,685,320 \text{ in³/hr}$

Thus, 1 cubic meter per second is equal to 219,685,320 cubic inches per hour.

Real-world Examples of Volume Flow Rates in m³/s:

1. A Large Industrial Water Pump:

   • A pump used to move water for irrigation or in a municipal water system can have a flow rate of around 2 cubic meters per second (m³/s).

2. River Flow:

   • A medium-sized river might have an average flow rate of about 100 cubic meters per second (m³/s).

3. Hydropower Turbines:

   • Large hydropower stations might operate turbines where the amount of water passing through is around 500 cubic meters per second (m³/s).

4. Water Treatment Plants:

   • A large modern water treatment facility might treat around 10 cubic meters of wastewater per second (m³/s).

5. Dams:

   • During peak spillway discharge events in large dams, flow rates might reach between 1,000 to 10,000 cubic meters per second (m³/s) or even more.

By understanding these figures and how to convert between different units, you can get a sense of the magnitude and applications of different flow rates in both natural and engineered systems.