How is CFM calculated from pressure


1.  Air Flow

Flow of air or any other fluid is caused by a pressure differential between two points.  Flow will originate from an area of high energy, or pressure, and proceed to area(s) of lower energy or pressure.

Duct air moves according to three fundamental laws of physics: conservation of mass, conservation of energy, and conservation of momentum.

Conservation of masssimply states that an air mass is neither created nor destroyed. From this principle it follows that the amount of air mass coming into a junction in a ductwork system is equal to the amount of air mass leaving the junction, or the sum of air masses at each junction is equal to zero. In most cases the air in a duct is assumed to be incompressible, an assumption that overlooks the change of air density that occurs as a result of pressure loss and flow in the ductwork. In ductwork, the law of conservation of mass means a duct size can be recalculated for a new air velocity using the simple equation:

V2 = (V1 * A1)/A2
Where V is velocity and A is Area

The law of energy conservation states that energy cannot disappear; it is only converted from one form to another. This is the basis of one of the main expression of aerodynamics, the Bernoulli equation. Bernoulli's equation in its simple form shows that, for an elemental flow stream, the difference in total pressures between any two points in a duct is equal to the pressure loss between these points, or:

(Pressure loss)1-2 = (Total pressure)1 - (Total pressure)2

Conservation of momentum is based on 's law that a body will maintain its state of rest or uniform motion unless compelled by another force to change that state. This law is useful to explain flow behavior in a duct system's fitting.

1.1.  Types of Flow

            Laminar Flow  

               Flow parallel to a boundary layer.  In HVAC system the plenum is a duct.

               Turbulent Flow 
Flow which is perpendicular and near the center of the duct and parallel near the outer edges of the duct.

               Most HVAC applications fall in the transition range between laminar and turbulent flow.


1.2.  Types of Pressure Losses or Resistance to Flow

Pressure loss is the loss of total pressure in a duct or fitting. There are three important observations that describe the benefits of using total pressure for duct calculation and testing rather than using only static pressure.

·        Only total pressure in ductwork always drops in the direction of flow. Static or dynamic pressures alone do not follow this rule.

·        The measurement of the energy level in an air stream is uniquely represented by total pressure only. The pressure losses in a duct are represented by the combined potential and kinetic energy transformation, i.e., the loss of total pressure.

·        The fan energy increases both static and dynamic pressure. Fan ratings based only on static pressure are partial, but commonly used.

Pressure loss in ductwork has three components, frictional losses along duct walls and dynamic losses in fittings and component losses in duct-mounted equipment.

Component Pressure

Due to physical items with known pressure drops, such as hoods, filters, louvers or dampers.

Dynamic Pressure

Dynamic losses are the result of changes in direction and velocity of air flow. Dynamic losses occur whenever an air stream makes turns, diverges, converges, narrows, widens, enters, exits, or passes dampers, gates, orifices, coils, filters, or sound attenuators. Velocity profiles are reorganized at these places by the development of vortexes that cause the transformation of mechanical energy into heat. The disturbance of the velocity profile starts at some distance before the air reaches a fitting. The straightening of a flow stream ends some distance after the air passes the fitting. This distance is usually assumed to be no shorter then six duct diameters for a straight duct. Dynamic losses are proportional to dynamic pressure and can be calculated using the equation:

Dynamic loss = (Local loss coefficient) * (Dynamic pressure)

where the Local loss coefficient, known as a C-coefficient, represents flow disturbances for particular fittings or for duct-mounted equipment as a function of their type and ratio of dimensions. Coefficients can be found in the ASHRAE Fittings diagrams.

A local loss coefficient can be related to different velocities; it is important to know which part of the velocity profile is relevant. The relevant part of the velocity profile is usually the highest velocity in a narrow part of a fitting cross section or a straight/branch section in a junction.

Frictional Pressure
Frictional losses in duct sections are result from air viscosity and momentum exchange among particles moving with different velocities.  These losses also contribute negligible losses or gains in air systems unless there are extremely long duct runs or there are significant sections using flex duct.

The easiest way of defining frictional loss per unit length is by using the Friction Chart (ASHRAE, 1997); however, this chart (shown below) should be used for elevations no higher of 500 m (1,600 ft), air temperature between 5°C and 40°C (40°F and 100°F), and ducts with smooth surfaces.  The Darcy-Weisbach Equation should be used for “non-standard” duct type such as flex duct.

Friction Chart   (ASHRAE HANDBOOK, 1997)
1.3.  Total Pressure, Velocity Pressure, and Static Pressure

It is convenient to calculate pressures in ducts using as a base an atmospheric pressure of zero. Mostly positive pressures occur in supply ducts and negative pressures occur in exhaust/return ducts; however, there are cases when negative pressures occur in a supply duct as a result of fitting effects.

Airflow through a duct system creates three types of pressures: static, dynamic (velocity), and total. Each of these pressures can be measured. Air conveyed by a duct system imposes both static and dynamic (velocity) pressures on the duct's structure. The static pressure is responsible for much of the force on the duct walls. However, dynamic (velocity) pressure introduces a rapidly pulsating load.

Static pressure
Static pressure is the measure of the potential energy of a unit of air in the particular cross section of a duct. Air pressure on the duct wall is considered static. Imagine a fan blowing into a completely closed duct; it will create only static pressure because there is no air flow through the duct.  A balloon blown up with air is a similar case in which there is only static pressure.

Dynamic (velocity) pressure
Dynamic pressure is the kinetic energy of a unit of air flow in an air stream. Dynamic pressure is a function of both air velocity and density:

Dynamic pressure = (Density) * (Velocity)2 / 2

The static and dynamic pressures are mutually convertible; the magnitude of each is dependent on the local duct cross section, which determines the flow velocity.

Total Pressure

Consists of the pressure the air exerts in the direction of flow (Velocity Pressure) plus the pressure air exerts perpendicular to the plenum or container through which the air moves.  In other words:

PT = PV + PS

PT = Total Pressure

PV = Velocity Pressure

PS =  Static Pressure

This general rule is used to derive what is called the Fan Total Pressure.  See the section entitled Fan Performance Specifications for a definition of Fan Total Pressure and Fan Static Pressure.




2.  Air Systems

For kitchen ventilation applications an air system consists of hood(s), duct work, and fan(s).  The relationship between the air flow rate (CFM) and the pressure of an air system is expressed as an increasing exponential function.  The graph below shows an example of a system curve.  This curve shows the relationship between the air flow rate and the pressure of an air system.

Complex systems with branches and junctions, duct size changes, and other variations can be broken into sections or sub-systems.  Each section or sub-system has its own system curve.  See the diagram below for an illustration of this concept.


2.1.  Fan Laws

Use the Fan Laws along a system curve.  If you know one (CFM, S.P.) point of a system you could use Fan Law 2 to determine the static pressure for other flow rates.  They apply to a fixed air system.  Once any element of the system changes, duct size, hood length, riser size, etc.. the system curve changes. 

                              CFM x        RPM x                                                              Fan Law 1

                              -------   =     -------

                              CFMknown   RPM known

                              SP x       CFM2 x        RPM2x                                                            Fan Law 2

                              ------  =   -------   =     -------

                              SPknown   CFM2known RPM2known

                              BHPx      CFM3x        RPM3x                                                            Fan Law 3

                              ------  =   -------   =      -------

                              BHPknown CFM3known  RPM3known

Other calculations can be utilized to maneuver around a fan performance curve.  For example, to calculate BHP from motor amp draw, use the following formula:

1 phase motors                                 3 phase motors

          BHP = V * I * E * PF                       BHP = V * I * E * PF * 1.73

                                                            746                                                      746

where:
               BHP = Brake Horsepower
               V = Line Voltage
               I = Line Current
               E = Motor Efficiency (Usually about .85 to .9)
               PF = Motor Power Factor (Usually about .9)

Once the BHP is known, the RPM of the fan can be measured.  The motor BHP and fan RPM can then be matched on the fan performance curve to approximate airflow.

2.2.  Air Density

The most common influences on air density are the effects of temperature other than 70 °F and barometric pressures other than 29.92” caused by elevations above sea level.

 

Ratings found in fan performance tables and curves are based on standard air.  Standard air is defined as clean, dry air with a density of 0.075 pounds per cubic foot, with the barometric pressure at sea level of 29.92 inches of mercury and a temperature of 70 °F.  Selecting a fan to operate at conditions other then standard air requires adjustment to both static pressure and brake horsepower.  The volume of air will not be affected in a given system because a fan will move the same amount of air regardless of the air density. In other words, if a fan will move 3,000 cfm at 70 °F it will also move 3,000 CFM at 250 °F.  Since 250 °F air weighs only 34% of 70°F air, the fan will require less BHP but it will also create less pressure than specified.

 

When a fan is specified for a given CFM and static pressure at conditions other than standard, the correction factors (shown in table below) must be applied in order to select the proper size fan, fan speed and BHP to meet the new condition.

 

The best way to understand how the correction factors are used is to work out several examples.  Let’s look at an example using a specification for a fan to operate at 600°F at sea level.  This example will clearly show that the fan must be selected to handle a much greater static pressure than specified.

 

Example #1:  A 20” centrifugal fan is required to deliver 5,000 cfm at 3.0 inches static pressure. Elevation is 0 (sea level).  Temperature is 600°F.  At standard conditions, the fan will require 6.76 bhp

 

1.            Using the chart below, the correction factor is 2.00.

2.            Multiply the specified operating static pressure by the correction factor to determine the standard air density equivalent static pressure.  (Corrected static pressure = 3.0 x 2.00 = 6”.  The fan must be selected for 6 inches of static pressure.)

3.            Based upon the performance table for a 20 fan at 5,000 cfm at 6 inches wg, 2,018 rpm is needed to produce the required performance.

4.            What is the operating bhp at 600 °F?

 

Since the horsepower shown in the performance chart refers to standard air density, this should be corrected to reflect actual bhp at the lighter operating air. 

Operating bhp = standard bhp ¸ 2.00 or 6.76 ¸ 2.00 = 3.38 bhp.

                   

2.3.  System Constant

Every air system or sub-system has a system constant.  This constant can be calculated as long as you know one (CFM, Static Pressure) point.   You use a variation of the fan laws to calculate the system constant.  To calculate the system constant:

                                            

K system = S.P./(CFM)2

Once you have the system constant you can calculate the static pressure for any flow rate.

                                            

S.P. = (CFM)2 * K system




3.  Pressure Losses of an Air System

Pressure losses are more easily determined by breaking an air system into sections.  Sections can be in series or in parallel.

3.1.  Sections in Series

For sections or components in series simply sum up all the sections. A single duct that has the same shape, cross section, and mass flow is called a duct section or just a section.

Following is the recommended procedure for calculating total pressure loss in a single duct section:

·