Cubic Centimeters per second (cm³/s) to Imperial Gallons per Second (imp-gal/s) conversion

What is Cubic Centimeters per second?

Cubic centimeters per second (cc/s or $\text{cm}^3/\text{s}$) is a unit of volumetric flow rate. It describes the volume of a substance that passes through a given area per unit of time. In this case, it represents the volume in cubic centimeters that flows every second. This unit is often used when dealing with small flow rates, as cubic meters per second would be too large to be practical.

Understanding Cubic Centimeters

A cubic centimeter ($cm^3$) is a unit of volume equivalent to a milliliter (mL). Imagine a cube with each side measuring one centimeter. The space contained within that cube is one cubic centimeter.

Defining "Per Second"

The "per second" part of the unit indicates the rate at which the cubic centimeters are flowing. So, 1 cc/s means one cubic centimeter of a substance is passing a specific point every second.

Formula for Volumetric Flow Rate

The volumetric flow rate (Q) can be calculated using the following formula:

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

Where:

• $Q$ = Volumetric flow rate (in $\text{cm}^3/\text{s}$)
• $V$ = Volume (in $\text{cm}^3$)
• $t$ = Time (in seconds)

Relationship to Other Units

Cubic centimeters per second can be converted to other units of flow rate. Here are a few common conversions:

• 1 $\text{cm}^3/\text{s}$ = 0.000001 $\text{m}^3/\text{s}$ (cubic meters per second)
• 1 $\text{cm}^3/\text{s}$ ≈ 0.061 $\text{in}^3/\text{s}$ (cubic inches per second)
• 1 $\text{cm}^3/\text{s}$ = 1 $\text{mL/s}$ (milliliters per second)

Applications in the Real World

While there isn't a specific "law" directly associated with cubic centimeters per second, it's a fundamental unit in fluid mechanics and is used extensively in various fields:

• Medicine: Measuring the flow rate of intravenous (IV) fluids, where precise and relatively small volumes are crucial. For example, administering medication at a rate of 0.5 cc/s.
• Chemistry: Controlling the flow rate of reactants in microfluidic devices and lab experiments. For example, dispensing a reagent at a flow rate of 2 cc/s into a reaction chamber.
• Engineering: Testing the flow rate of fuel injectors in engines. Fuel injector flow rates are critical and are measured in terms of volume per time, such as 15 cc/s.
• 3D Printing: Regulating the extrusion rate of material in some 3D printing processes. The rate at which filament extrudes could be controlled at levels of 1-5 cc/s.
• HVAC Systems: Measuring air flow rates in small ducts or vents.

Relevant Physical Laws and Concepts

The concept of cubic centimeters per second ties into several important physical laws:

• Continuity Equation: This equation states that for incompressible fluids, the mass flow rate is constant throughout a closed system. The continuity equation is expressed as:

  $A_1v_1 = A_2v_2$

  where $A$ is the cross-sectional area and $v$ is the flow velocity.

  Khan Academy's explanation of the Continuity Equation further details the relationship between area, velocity, and flow rate.

• Bernoulli's Principle: This principle relates the pressure, velocity, and height of a fluid in a flowing system. It states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

  More information on Bernoulli's Principle can be found here.

What is the Imperial Gallon per Second?

The Imperial gallon per second (imp-gal/s) is a unit of volumetric flow rate, expressing the volume of liquid passing a point each second measured in Imperial (UK) gallons. It appears in British and Commonwealth engineering contexts such as pump ratings, water supply, and fuel handling.

Definition

One Imperial gallon per second equals one Imperial gallon of volume flowing every second. Since the Imperial gallon is defined as exactly 4.54609 litres, the flow rate converts directly to litres per second:

$$1\ \text{imp-gal/s} = 4.54609\ \text{l/s}$$

The Imperial gallon is fixed by definition as 4.54609 L exactly (originally the volume of 10 pounds of water). This makes it noticeably larger than the US liquid gallon of 3.785411784 L, so an Imperial gallon per second delivers about 20% more volume than a US gallon per second.

Origin and History

The Imperial gallon was established by the British Weights and Measures Act of 1824, defined as the volume of ten pounds of distilled water at 62 °F. In 1985 the UK redefined it in metric terms as exactly 4.54609 litres. As a rate unit, gallons per second and the more common gallons per minute grew out of the need to specify pump and pipe throughput during the industrial era.

Law and Notable Facts

The Imperial gallon remains a legally recognised unit in the United Kingdom, though the litre is the primary trading unit under metrication. It is distinct from the US gallon: the Imperial gallon (4.54609 L) is roughly 20% larger than the US liquid gallon (3.785 L), so flow figures quoted in "gallons" must always specify which system. A flow of 1 imp-gal/s corresponds to 60 Imperial gallons per minute or 3,600 per hour.

Real-World Examples and Conversions

• A flow of 1 imp-gal/s equals 4.54609 L/s, or about 272.77 litres per minute.
• A typical domestic garden hose delivers well under 1 imp-gal/s; a rate of 1 imp-gal/s (≈16,366 L/h) is closer to a small industrial or firefighting pump.
• 1 imp-gal/s ≈ 1.20095 US gallons per second, reflecting the larger Imperial gallon.
• 1 imp-gal/s ≈ 0.00454609 cubic metres per second, useful when comparing against SI pump specifications.