Cubic Decimeters per second (dm³/s) to Millilitres per second (ml/s) conversion

What is Cubic Decimeters per second?

This document explains cubic decimeters per second, a unit of volume flow rate. It will cover the definition, formula, formation, real-world examples and related interesting facts.

Definition of Cubic Decimeters per Second

Cubic decimeters per second ($dm^3/s$) is a unit of volume flow rate in the International System of Units (SI). It represents the volume of fluid (liquid or gas) that passes through a given cross-sectional area per second, where the volume is measured in cubic decimeters. One cubic decimeter is equal to one liter.

Formation and Formula

The unit is formed by dividing a volume measurement (cubic decimeters) by a time measurement (seconds). The formula for volume flow rate ($Q$) can be expressed as:

$$Q = \frac{V}{t}$$

Where:

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

An alternative form of the equation is:

$$Q = A \cdot v$$

Where:

• $Q$ is the volume flow rate ($dm^3/s$)
• $A$ is the cross-sectional area ($dm^2$)
• $v$ is the average velocity of the flow ($dm/s$)

Conversion

Here are some useful conversions:

• $1 \frac{dm^3}{s} = 0.001 \frac{m^3}{s}$
• $1 \frac{dm^3}{s} = 1 \frac{L}{s}$ (Liters per second)
• $1 \frac{dm^3}{s} \approx 0.0353 \frac{ft^3}{s}$ (Cubic feet per second)

Real-World Examples

• Water Flow in Pipes: A small household water pipe might have a flow rate of 0.1 to 1 $dm^3/s$ when a tap is opened.
• Medical Infusion: An intravenous (IV) drip might deliver fluid at a rate of around 0.001 to 0.01 $dm^3/s$.
• Small Pumps: Small water pumps used in aquariums or fountains might have flow rates of 0.05 to 0.5 $dm^3/s$.
• Industrial Processes: Some chemical processes or cooling systems might involve flow rates of several $dm^3/s$.

Interesting Facts

• The concept of flow rate is fundamental in fluid mechanics and is used extensively in engineering, physics, and chemistry.
• While no specific law is directly named after "cubic decimeters per second," the principles governing fluid flow are described by various laws and equations, such as the continuity equation and Bernoulli's equation. These are explored in detail in fluid dynamics.

For a better understanding of flow rate, you can refer to resources like Khan Academy's Fluid Mechanics section.

What is millilitres per second?

Millilitres per second (mL/s) is a unit of volumetric flow rate, describing the volume of fluid that passes through a given point per unit of time. It's commonly used in various fields where precise measurement of small fluid volumes is essential.

Definition of Millilitres per Second

Millilitres per second (mL/s) is a derived unit. It combines the metric unit of volume, the milliliter (mL), with the SI unit of time, the second (s). One milliliter is equal to one cubic centimeter ($1 \text{ mL} = 1 \text{ cm}^3$). Therefore, 1 mL/s is equivalent to 1 cubic centimeter of fluid flowing past a point in one second.

How Millilitres per Second is Formed

The unit is formed by expressing volume in milliliters and dividing it by time in seconds.

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

$$\text{Flow Rate (mL/s)} = \frac{\text{Volume (mL)}}{\text{Time (s)}}$$

Common Applications and Examples

• Medical Applications: Infusion pumps deliver medication at precise rates, often measured in mL/s. For instance, a doctor might prescribe an IV drip at a rate of 0.5 mL/s.
• Laboratory Experiments: Chemical reactions and experiments often require precise control over the flow of liquids. Microfluidic devices frequently operate in the mL/s range or even lower.
• Small Engine Fuel Consumption: The fuel consumption of a small engine, like a lawnmower, can be expressed in mL/s. For example, an engine might consume 2 mL/s of gasoline at idle.
• 3D Printing: In material extrusion 3D printing, the flow rate of the melted filament is often controlled and can be expressed in mL/s.
• Water flow from faucets: A slowly dripping faucet might release water at a rate of approximately 0.1 mL/s. A fully open faucet might release water at a rate of 200 mL/s.

Relationship to Other Units

Millilitres per second can be converted to other volumetric flow rate units:

• Liters per second (L/s): 1 L/s = 1000 mL/s
• Cubic meters per second ($m^3/s$): 1 $m^3/s$ = 1,000,000 mL/s
• Gallons per minute (GPM): 1 GPM ≈ 0.0630902 L/s ≈ 63.0902 mL/s

Notable Figures and Laws

While no specific law is directly associated with milliliters per second, the concept of flow rate is fundamental in fluid dynamics. Key figures in this field include:

• Daniel Bernoulli: Known for Bernoulli's principle, which relates fluid speed to pressure.
• Osborne Reynolds: Known for the Reynolds number, which helps predict flow patterns in fluids.

For further reading on fluid dynamics, refer to Introduction to Fluid Dynamics on The LibreTexts libraries.