Cubic kilometers per second to Cubic inches per hour conversion

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

To convert cubic kilometers per second (km³/s) to cubic inches per hour (in³/hr), we need to use a series of unit conversions. Let's break it down step by step.

Conversion Steps:

1. Convert cubic kilometers to cubic meters:

   • 1 km³ = (1000 meters)³ = 1,000,000,000 m³ (1 billion cubic meters).

2. Convert cubic meters to cubic centimeters:

   • 1 m³ = (100 cm)³ = 1,000,000 cm³ (1 million cubic centimeters).
   • Therefore, 1 km³ = 1,000,000,000 m³ * 1,000,000 cm³/m³ = 1,000,000,000,000,000 (10^15) cm³.

3. Convert cubic centimeters to cubic inches:

   • 1 inch = 2.54 cm, so 1 in³ = (2.54 cm)³ ≈ 16.387 cm³.
   • Therefore, 1 cm³ ≈ 1/16.387 in³ ≈ 0.0610237 in³.
   • Therefore, 10¹⁵ cm³ * 0.0610237 in³/cm³ ≈ 6.10237 * 10¹³ in³.

4. Convert seconds to hours:

   • 1 hour = 3600 seconds.

5. Combine both conversions:

   • 1 km³/s = 6.10237 * 10¹³ in³/s.
   • 6.10237 * 10¹³ in³/s * 3600 s/hr ≈ 2.19725 * 10¹⁷ in³/hr.

So, 1 km³/s is approximately equal to 2.19725 * 10¹⁷ cubic inches per hour.

Real-World Examples:

1. Amazon River:

   • The Amazon River has an average discharge rate of about 0.209 km³/s, which would translate to approximately 4.597 * 10¹⁶ in³/hr.

2. Water usage of a city:

   • A large city might use around 0.00002 km³/s (or 20,000 liters per second). This translates to approximately 4.3945 * 10¹² in³/hr.

3. Bursting of a dam:

   • Consider a hypothetical scenario where a large dam bursts releasing water at 0.5 km³/s initially. This flow would be about 1.1 * 10¹⁷ in³/hr.

4. Volcanic eruption:

   • During the 1980 eruption of Mount St. Helens, the volume of material erupted was approximately 1 km³ over several seconds, equivalent to a flow rate of 1 km³/s if it happened in one second.

These examples help illustrate how massive 1 cubic kilometer per second is and provide a sense of scale for such large volume flow rates. The quantities involved are enormous and typically pertain to natural events or large-scale industrial processes.