Cubic kilometers per second to Gallons per minute conversion

How to convert cubic kilometers per second to gallons per minute?

To convert from cubic kilometers per second (km³/s) to gallons per minute (gal/min), follow these steps:

1. Convert cubic kilometers to cubic meters: $1 \text{ km}^3 = 1,000,000,000 \text{ m}^3 = 10^9 \text{ m}^3$

2. Convert cubic meters to liters: $1 \text{ m}^3 = 1,000 \text{ liters}$ $1 \text{ km}^3 = 1,000,000,000 \text{ m}^3 \times 1,000 \text{ liters/m}^3 = 10^{12} \text{ liters}$

3. Convert liters to gallons: $1 \text{ liter} \approx 0.264172 \text{ gallons}$ $10^{12} \text{ liters} \times 0.264172 \text{ gallons/liter} \approx 2.64172 \times 10^{11} \text{ gallons}$

4. Convert seconds to minutes: $1 \text{ minute} = 60 \text{ seconds}$

5. Combine the conversions: Since we have the volume in gallons and time in seconds: $\frac{2.64172 \times 10^{11} \text{ gallons}}{1 \text{ second}} \times \frac{60 \text{ seconds}}{1 \text{ minute}} = 2.64172 \times 10^{11} \times 60 \text{ gal/min} \approx 1.58503 \times 10^{13} \text{ gal/min}$

So, 1 cubic kilometer per second (km³/s) is approximately 1.58503 \times 10^{13} gallons per minute (gal/min).

Real-world examples:

• Amazon River: The Amazon River has an average discharge of about 209,000 cubic meters per second (m³/s) which translates to about 0.000209 km³/s. Converting this to gallons per minute: $0.000209 \text{ km}^3/\text{s} \times 1.58503 \times 10^{13} \text{ gal/min per km}^3/\text{s} \approx 3.311 \times 10^9 \text{ gal/min}$

• Niagara Falls: The average flow rate of water going over Niagara Falls is about 2,400 cubic meters per second (m³/s), approximately 0.0024 km³/s. Converting this to gallons per minute: $0.0024 \text{ km}^3/\text{s} \times 1.58503 \times 10^{13} \text{ gal/min per km}^3/\text{s} \approx 3.804 \times 10^{10} \text{ gal/min}$

• Large-scale desalination plant: As a theoretical example, let's say a very large desalination plant produces 0.00001 km³/s (10,000 cubic meters per second). Converting this to gallons per minute: $0.00001 \text{ km}^3/\text{s} \times 1.58503 \times 10^{13} \text{ gal/min per km}^3/\text{s} \approx 1.58503 \times 10^8 \text{ gal/min}$

These conversions highlight the extremely large volume flow rates represented by terms involving cubic kilometers per second, especially when contextualized into gallons per minute which is a more commonly used unit in daily activities and infrastructure scenarios.