Millimeters per hour to Metres per second conversion

How to convert millimeters per hour to metres per second?

To convert from millimeters per hour (mm/h) to meters per second (m/s), we need to take into account two conversion factors:

1. There are 1,000 millimeters in a meter.
2. There are 3,600 seconds in an hour.

Given the conversion factors, we can derive the formula:

$\text{1 mm/h} = \left( \frac{1 \text{ mm}}{1 \text{ hour}} \right) \times \left( \frac{1 \text{ meter}}{1000 \text{ mm}} \right) \times \left( \frac{1 \text{ hour}}{3600 \text{ seconds}} \right)$

Simplify the equation:

$\text{1 mm/h} = \frac{1}{1000} \times \frac{1}{3600} \text{ m/s}$ $\text{1 mm/h} = \frac{1}{3,600,000} \text{ m/s}$

Finally:

$\text{1 mm/h} = 2.777 \times 10^{-7} \text{ m/s}$

Real World Examples

1. 10 mm/h: $10 \text{ mm/h} = 10 \times 2.777 \times 10^{-7} \text{ m/s}$ $10 \text{ mm/h} = 2.777 \times 10^{-6} \text{ m/s}$

2. 50 mm/h: $50 \text{ mm/h} = 50 \times 2.777 \times 10^{-7} \text{ m/s}$ $50 \text{ mm/h} = 1.3885 \times 10^{-5} \text{ m/s}$

3. 100 mm/h: $100 \text{ mm/h} = 100 \times 2.777 \times 10^{-7} \text{ m/s}$ $100 \text{ mm/h} = 2.777 \times 10^{-5} \text{ m/s}$

Real World Contexts

• Rainfall Rates: Rainfall might be measured in millimeters per hour. Converting this to meters per second can help in understanding the intensity in different units. For instance, a light drizzle might be around 1 mm/h, while a heavy rainfall could exceed 50 mm/h.

• Slow Geological Movements: The pace at which tectonic plates move can sometimes be measured in mm/h. These movements are extremely slow, typically on the order of mm/year, so mm/h can be a useful intermediate step for geologists.

• Manufacturing Processes: In precision manufacturing, machinery might advance feed materials or tools at rates measured in mm/h, especially for extremely delicate or slow processes.

By understanding these conversions, you can contextualize and compare these rates within various fields and practical scenarios.