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Cubic Millimeters per second (mm³/s) to Cubic meters per minute (m³/min) conversion

Cubic Millimeters per second to Cubic meters per minute conversion table

Cubic Millimeters per second (mm³/s)	Cubic meters per minute (m³/min)
0	0
1	6e-8
2	1.2e-7
3	1.8e-7
4	2.4e-7
5	3e-7
6	3.6e-7
7	4.2e-7
8	4.8e-7
9	5.4e-7
10	6e-7
20	0.0000012
30	0.0000018
40	0.0000024
50	0.000003
60	0.0000036
70	0.0000042
80	0.0000048
90	0.0000054
100	0.000006
1000	0.00006

How to convert cubic millimeters per second to cubic meters per minute?

Here's a guide on converting between cubic millimeters per second ( $mm^3/s$ ) and cubic meters per minute ( $m^3/min$ ).

Understanding Volume Flow Rate Conversion

Converting between different units of volume flow rate involves understanding the relationships between the units of volume (cubic millimeters vs. cubic meters) and the units of time (seconds vs. minutes). We'll break down the conversion process step by step.

Converting Cubic Millimeters per Second to Cubic Meters per Minute

Here's how to convert from $mm^3/s$ to $m^3/min$ :

Volume Conversion: Convert cubic millimeters ( $mm^3$ ) to cubic meters ( $m^3$ ).
- $1 m = 1000 mm$
- Therefore, $1 m^3 = (1000 mm)^3 = 10^9 mm^3$
- So, $1 mm^3 = 10^{-9} m^3$
Time Conversion: Convert seconds ( $s$ ) to minutes ( $min$ ).
- $1 min = 60 s$
- Therefore, $1 s = \frac{1}{60} min$
Combining the Conversions:
- To convert $1 mm^3/s$ to $m^3/min$ , multiply by the conversion factors:
  
  $1 \frac{mm^3}{s} = 1 \frac{mm^3}{s} \times \frac{1 m^3}{10^9 mm^3} \times \frac{60 s}{1 min}$
  
  $1 \frac{mm^3}{s} = \frac{60}{10^9} \frac{m^3}{min}$
  
  $1 \frac{mm^3}{s} = 6 \times 10^{-8} \frac{m^3}{min}$
Therefore, 1 cubic millimeter per second is equal to $6 \times 10^{-8}$ cubic meters per minute.

Converting Cubic Meters per Minute to Cubic Millimeters per Second

Now, let's convert from $m^3/min$ to $mm^3/s$ :

Volume Conversion: Convert cubic meters ( $m^3$ ) to cubic millimeters ( $mm^3$ ).
- $1 m^3 = 10^9 mm^3$
Time Conversion: Convert minutes ( $min$ ) to seconds ( $s$ ).
- $1 min = 60 s$
- Therefore, $1 s = \frac{1}{60} min$ or $1 min = 60 s$
Combining the Conversions:
- To convert $1 m^3/min$ to $mm^3/s$ , multiply by the conversion factors:
  
  $1 \frac{m^3}{min} = 1 \frac{m^3}{min} \times \frac{10^9 mm^3}{1 m^3} \times \frac{1 min}{60 s}$
  
  $1 \frac{m^3}{min} = \frac{10^9}{60} \frac{mm^3}{s}$
  
  $1 \frac{m^3}{min} = 1.66666667 \times 10^{7} \frac{mm^3}{s}$
Therefore, 1 cubic meter per minute is equal to $1.66666667 \times 10^{7}$ cubic millimeters per second.

Real-World Examples

While direct conversions from cubic millimeters per second to cubic meters per minute might not be commonly used in everyday conversation, understanding volume flow rates is essential in various fields:

Medical Science: Infusion rates of intravenous fluids can be measured in $mL/hr$ (milliliters per hour), which can be converted to $mm^3/s$ for precise calculations in drug delivery systems.
Engineering: Water flow in small pipes.
Environmental Science: Measuring very low flow rates in environmental studies.

Historical Context and Notable Figures

While there isn't a specific law or well-known person directly associated with this particular conversion, the standardization of units of measurement has been a gradual process involving numerous scientists and mathematicians. The development of the metric system, which forms the basis for these conversions, can be attributed to the French Revolution and the subsequent efforts of scientists to create a universal system of measurement. Key figures include:

Antoine Lavoisier: A French chemist who contributed to the development of the metric system before his execution during the French Revolution.
Marquis de Condorcet: A mathematician and philosopher who played a significant role in advocating for the adoption of a decimal-based system of measurement.

Standardized measurement systems are essential for ensuring accuracy and consistency in scientific research, engineering, and trade. The metric system, with its base-10 structure, simplifies conversions and promotes international collaboration.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the Cubic meters per minute to other unit conversions.

What is Cubic Millimeters per Second?

Cubic millimeters per second ( $mm^3/s$ ) is a unit of volumetric flow rate, indicating the volume of a substance passing through a specific area each second. It's a measure of how much volume flows within a given time frame. This unit is particularly useful when dealing with very small flow rates.

Formation of Cubic Millimeters per Second

The unit $mm^3/s$ is derived from the base units of volume (cubic millimeters) and time (seconds).

Cubic Millimeter ( $mm^3$ ): A cubic millimeter is a unit of volume, representing a cube with sides that are each one millimeter in length.
Second (s): The second is the base unit of time in the International System of Units (SI).

Combining these, $mm^3/s$ expresses the volume in cubic millimeters that flows or passes through a point in one second.

Flow Rate Formula

The flow rate ( $Q$ ) can be defined mathematically as:

Q = \frac{V}{t}

Where:

$Q$ is the flow rate ( $mm^3/s$ ).
$V$ is the volume ( $mm^3$ ).
$t$ is the time (s).

This formula indicates that the flow rate is the volume of fluid passing through a cross-sectional area per unit time.

Applications and Examples

While $mm^3/s$ might seem like a very small unit, it's applicable in several fields:

Medical Devices: Infusion pumps deliver medication at precisely controlled, often very slow, flow rates. For example, a pump might deliver insulin at a rate of 5 $mm^3/s$ .
Microfluidics: In microfluidic devices, used for lab-on-a-chip applications, reagents flow at very low rates. Reactions can be studied using flow rates of 1 $mm^3/s$ .
3D Printing: Some high resolution 3D printers using resin operate by very slowly dispensing material. The printer can be said to be pushing out material at 2 $mm^3/s$ .

Relevance to Fluid Dynamics

Cubic millimeters per second relates directly to fluid dynamics, particularly in scenarios involving low Reynolds numbers, where flow is laminar and highly controlled. This is essential in applications requiring precision and minimal turbulence. You can learn more about fluid dynamics at Khan Academy's Fluid Mechanics Section.

What is cubic meters per minute?

Cubic meters per minute ( $m^3/min$ ) is a unit used to express volume flow rate, indicating the volume of a substance that passes through a specific area per minute. It's commonly used to measure fluid flow rates in various applications.

Understanding Cubic Meters per Minute

Cubic meters per minute is derived from two fundamental SI units: volume (cubic meters, $m^3$ ) and time (minutes, min). One cubic meter is the volume of a cube with sides of one meter in length.

The Formula for Volume Flow Rate

Volume flow rate ( $Q$ ) is defined as the volume ( $V$ ) of a fluid passing through a cross-sectional area per unit of time ( $t$ ).

Q = \frac{V}{t}