The Math Behind Air Flow

THE MATH BEHIND AIR FLOW

Air Flow
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.
Air Flow Cont.
Conservation of mass simply 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
Types Of Flow
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.
Types Of Pressure Losses / Resistance
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.
Component Pressure
Component Pressure Due to physical items with known pressure drops, such as hoods, filters, louvers or dampers. Dynamic Pressure Component Pressure Due to physical items with known pressure drops, such as hoods, filters, louvers or dampers.
Dynamic Pressure
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.
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Frictional Pressure
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.
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Darcy-Weisbach Equation
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.
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.

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