Cubic Millimeters per second to Cubic yards per hour conversion

How to convert cubic millimeters per second to cubic yards per hour?

To convert cubic millimeters per second (mm³/s) to cubic yards per hour (yd³/h), you need to follow a series of unit conversions.

Let's break down the conversion steps:

1. Convert cubic millimeters to cubic meters.
2. Convert cubic meters to cubic yards.
3. Convert seconds to hours.

Conversion Factors:

• Cubic Millimeters to Cubic Meters: 1 cubic meter = $1 \times 10^9$ cubic millimeters $1 \text{ mm³} = 1 \times 10^{-9} \text{ m³}$

• Cubic Meters to Cubic Yards: 1 cubic meter ≈ 1.30795 cubic yards $1 \text{ m³} ≈ 1.30795 \text{ yd³}$

• Seconds to Hours: 1 hour = 3600 seconds

Conversion Steps:

1. Convert 1 mm³/s to m³/s: $1 \text{ mm³/s} \times 1 \times 10^{-9} \text{ m³/mm³} = 1 \times 10^{-9} \text{ m³/s}$

2. Convert m³/s to yd³/s: $1 \times 10^{-9} \text{ m³/s} \times 1.30795 \text{ yd³/m³} ≈ 1.30795 \times 10^{-9} \text{ yd³/s}$

3. Convert yd³/s to yd³/h: $1.30795 \times 10^{-9} \text{ yd³/s} \times 3600 \text{ s/h} ≈ 4.70862 \times 10^{-6} \text{ yd³/h}$

Therefore, 1 cubic millimeter per second is approximately $4.70862 \times 10^{-6}$ cubic yards per hour.

Real-World Examples for Other Quantities of Cubic Millimeters per Second:

1. Raindrop Discharge: Suppose a small gutter drains water at a rate of 50,000 mm³/s. To convert this to cubic yards per hour: $50,000 \text{ mm³/s} \times 4.70862 \times 10^{-6} \text{ yd³/h per mm³/s} ≈ 0.235431 \text{ yd³/h}$

2. Syringe Flow in a Medical Scenario: If a medical pump delivers medication at a rate of 1,000 mm³/s: $1,000 \text{ mm³/s} \times 4.70862 \times 10^{-6} \text{ yd³/h per mm³/s} ≈ 0.004709 \text{ yd³/h}$

3. Industrial Pipeline: An industrial pipeline might transport oil at a rate of 1,000,000 mm³/s: $1,000,000 \text{ mm³/s} \times 4.70862 \times 10^{-6} \text{ yd³/h per mm³/s} ≈ 4.70862 \text{ yd³/h}$

In these examples, you can see how different flow rates scale when converting from cubic millimeters per second to cubic yards per hour.