Cubic feet per hour (ft³/h) to Cubic Centimeters per second (cm³/s) conversion

What is Cubic feet per hour?

Cubic feet per hour (CFH) is a unit used to measure the volumetric flow rate. It represents the volume of a substance (gas or liquid) that passes through a specific area per hour, measured in cubic feet. It's a common unit in various fields, especially when dealing with gas and air flow.

Definition of Cubic Feet per Hour

Cubic feet per hour (CFH) is defined as the volume of a substance, measured in cubic feet, that flows past a point in one hour.

$$1 \text{ CFH} = 1 \frac{\text{ft}^3}{\text{hour}}$$

How CFH is Formed

CFH is derived from the basic units of volume (cubic feet) and time (hour). It directly expresses how many cubic feet of a substance move within one hour. No special law or constant is specifically tied to the definition of CFH itself. It is a direct measure of flow rate, useful in practical applications.

Calculating Volume Flow Rate

The volume flow rate (Q) in cubic feet per hour can be determined using the following formula:

$$Q = A \cdot v$$

Where:

• $Q$ = Volume flow rate (ft³/hour)
• $A$ = Cross-sectional area of the flow (ft²)
• $v$ = Average velocity of the flow (ft/hour)

Another way to calculate it is:

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

Where:

• $Q$ = Volume flow rate (ft³/hour)
• $V$ = Volume (ft³)
• $t$ = Time (hours)

Real-World Examples of CFH

• Natural Gas Consumption: Home appliances like furnaces, water heaters, and stoves are rated in terms of CFH to indicate their natural gas consumption. A typical furnace might consume 80-120 CFH of natural gas.
• HVAC Systems: Air conditioning and ventilation systems use CFH to measure the airflow rate in ductwork. A residential HVAC system might require airflow rates between 400 and 1600 CFH, depending on the size of the home.
• Compressed Air Systems: Pneumatic tools and equipment in factories use compressed air. The compressor output is often rated in CFH or cubic feet per minute (CFM, which can easily be converted to CFH by multiplying by 60) to indicate the volume of air it can supply.
• Industrial Processes: Many industrial processes, such as chemical manufacturing or food processing, involve controlling the flow rate of liquids or gases. CFH can be used to specify the desired flow rate of a particular fluid. For example, a chemical reactor might require a flow of 50 CFH of nitrogen gas.
• Ventilation Systems: Exhaust fans in bathrooms or kitchens are often rated in CFM (cubic feet per minute), which can be converted to CFH. A typical bathroom exhaust fan might be rated at 50-100 CFM, which equals 3000-6000 CFH.

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.