Cubic Millimeters per second to Gallons per hour conversion

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

Certainly! To convert cubic millimeters per second (mm³/s) to gallons per hour (gal/h), you need to use unit conversion factors that relate these two volume flow rates.

Here's a step-by-step process to convert 1 cubic millimeter per second (mm³/s) to gallons per hour (gal/h):

1. Convert cubic millimeters to cubic meters: 1 mm³ = 1e-9 cubic meters (m³).

2. Convert cubic meters to liters: 1 m³ = 1000 liters.

3. Convert liters to gallons: 1 liter ≈ 0.264172 gallons (in the US customary system).

4. Convert seconds to hours: 1 second = 1/3600 hours.

Now let's put it all together: $1 \text{ mm}^3/\text{s} \times \frac{1 \text{ m}^3}{1 \times 10^9 \text{ mm}^3} \times \frac{1000 \text{ L}}{1 \text{ m}^3} \times \frac{0.264172 \text{ gal}}{1 \text{ L}} \times \frac{3600 \text{ s}}{1 \text{ hr}}$

Simplifying this: $1 \times 10^{-9} \text{ m}^3/\text{s} \times 1000 \text{ L}/\text{m}^3 \times 0.264172 \text{ gal}/\text{L} \times 3600 \text{ s}/\text{hr}$ $= 1 \times 10^{-9} \times 1000 \times 0.264172 \times 3600$ $= 9.5106 \times 10^{-4} \text{ gal/h}$

So, 1 cubic millimeter per second is approximately 0.00095106 gallons per hour.

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

1. 10 mm³/s: $10 \text{ mm}^3/\text{s} \times 9.5106 \times 10^{-4} \text{ gal/hr} = 0.0095106 \text{ gal/hr}$

   • Comparable to a very slow drip from a leaking faucet.

2. 100 mm³/s: $100 \text{ mm}^3/\text{s} \times 9.5106 \times 10^{-4} \text{ gal/hr} = 0.095106 \text{ gal/hr}$

   • Roughly similar to the rate of water seeping out of a slightly larger leak, about a tablespoon per minute.

3. 1000 mm³/s (1 cm³/s or 1 mL/s): $1000 \text{ mm}^3/\text{s} \times 9.5106 \times 10^{-4} \text{ gal/hr} = 0.95106 \text{ gal/hr}$

   • This is closer to a consistent trickle, which might come from a slightly open faucet.

4. 5000 mm³/s: $5000 \text{ mm}^3/\text{s} \times 9.5106 \times 10^{-4} \text{ gal/hr} = 4.7553 \text{ gal/hr}$

   • This could compare to a small but steady flow, similar to a garden hose running at a low rate.

5. 10000 mm³/s (10 cm³/s or 10 mL/s): $10000 \text{ mm}^3/\text{s} \times 9.5106 \times 10^{-4} \text{ gal/hr} = 9.5106 \text{ gal/hr}$

   • Comparable to a moderate stream, such as water flowing out of a kitchen sink faucet.

These conversions and examples help provide context for the magnitude of flow rates in cubic millimeters per second when considered in more familiar terms like gallons per hour.