Kilolitres per hour to Cubic kilometers per second conversion

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

Converting kilolitres per hour (kL/h) to cubic kilometers per second (km³/s) involves several steps, as these units are vastly different in scale. Let's break this down:

1. Understanding the Units:

   • Kilolitre (kL): 1 kilolitre is equivalent to 1,000 liters.
   • Cubic Kilometer (km³): 1 cubic kilometer equals 1,000,000,000,000 liters (10¹² liters).
   • Hour to Second Conversion: 1 hour is equivalent to 3,600 seconds.

2. Conversion Process:

   • First, convert kilolitres to liters.
   • Then, convert liters to cubic kilometers.
   • Lastly, adjust the time conversion from hours to seconds.

Here is the step-by-step conversion:

1. Start with the given rate: 1 kL/h.
2. Convert 1 kL to liters: $1 \text{ kL} = 1,000 \text{ liters}$
3. Convert liters to cubic kilometers: $1,000 \text{ liters} \times \left( \frac{1 \text{ km}^3}{10^{12} \text{ liters}} \right) = 1,000 \times 10^{-12} \text{ km}^3 = 10^{-9} \text{ km}^3$
4. Adjust for time from hours to seconds: $10^{-9} \text{ km}^3 \text{ per hour} \times \left( \frac{1 \text{ hour}}{3,600 \text{ seconds}} \right) = 10^{-9} \div 3,600 \text{ km}^3/\text{s}$ $= 2.78 \times 10^{-13} \text{ km}^3/\text{s}$

So, 1 kL/h is equivalent to $2.78 \times 10^{-13}$ km³/s.

Real World Examples

1. Municipal Water Supply:

   • A small town's water treatment plant may process around 500 kL/h, which is about $1.39 \times 10^{-10}$ km³/s.

2. Industrial Usage:

   • A large factory might consume about 1,000 kL/h of water, converting to $2.78 \times 10^{-10}$ km³/s.

3. River Flow Rate:

   • A medium-sized river might have a flow rate of 50,000 kL/h, equivalent to $1.39 \times 10^{-8}$ km³/s.

4. Large Dam Discharge:

   • A significant dam could discharge around 200,000 kL/h of water, resulting in approximately $5.56 \times 10^{-8}$ km³/s.

These examples illustrate how varying scales of kilolitres per hour are used in different contexts, showcasing the versatility of this measure in real-world applications.