Cubic Millimeters per second (mm³/s) to Cubic inches per second (in³/s) conversion

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 Inches per Second?

Cubic inches per second (in$^3$/s) is a unit of flow rate that expresses the volume of a substance passing through a cross-sectional area per unit time. Specifically, it measures how many cubic inches of a substance flow past a point in one second.

Formation of Cubic Inches per Second

This unit is derived from the fundamental units of volume (cubic inches) and time (seconds). It's a volumetric flow rate, calculated as:

$$\text{Flow Rate} = \frac{\text{Volume}}{\text{Time}}$$

In this case:

• Volume is measured in cubic inches (in$^3$). 1 cubic inch is equal to $16.3871 \text{ cm}^3$.
• Time is measured in seconds (s).

Therefore, 1 in$^3$/s means that one cubic inch of a substance flows past a specific point in one second.

Real-World Applications and Examples

Understanding the scale of cubic inches per second is easier with real-world examples:

• Small Engine Displacement: The displacement of small engines, like those in lawnmowers or motorcycles, can be expressed in cubic inches. While not directly a flow rate, it represents the total volume displaced by the pistons during one engine cycle, influencing performance. A larger displacement generally means more power.

• Hydraulic Systems: In hydraulic systems, such as those used in heavy machinery or braking systems, flow rates are crucial. The rate at which hydraulic fluid flows through valves and cylinders, often measured in gallons per minute (GPM), can be converted to cubic inches per second to ensure precise control and operation. One GPM equals 0.0631 in$^3$/s

• Fuel Injectors: Fuel injectors in internal combustion engines control the flow of fuel into the cylinders. The flow rate of fuel injectors is critical for engine performance and emissions. While often measured in other units, these rates can be converted to cubic inches per second for comparison.

• HVAC Systems: Airflow in heating, ventilation, and air conditioning (HVAC) systems is often measured in cubic feet per minute (CFM). CFM can be converted to cubic inches per second to quantify the amount of air being circulated. One CFM equals 1.728 in$^3$/s

Interesting Facts and Related Concepts

• Dimensional Analysis: When working with flow rates, dimensional analysis is crucial to ensure consistent units. Converting between different units of volume and time (e.g., gallons per minute to cubic inches per second) requires careful attention to conversion factors.

• Fluid Dynamics: The study of fluid dynamics relies heavily on the concept of flow rate. Principles like the conservation of mass and Bernoulli's equation are used to analyze and predict fluid behavior in various systems. Bernoulli's principle is a statement about conservation of energy for fluids.