Basic Duct Hydraulics

8/13/2019 Basic Duct Hydraulics

1/4

1/9/12 Basic Duct Hy draulics

1/4ateam.lbl.gov/D esign-Guide/DGHtm/basicducthy draulics.htm

Basic Duct Hydraulics

Duct air moves according to three fundamental laws of physics: conservation of mass,

conservation of energy, and conservation of momentum.

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, anassumption that overlooks the change of air density that occurs as a result of pressure loss and

flow in the ductwork. In round ductwork, the law of conservation of mass means a duct

diameter can be recalculated for a new air velocity using the simple equation:

Diameter2 = Diameter1 (Velocity1 / Velocity2)0.5

or the air velocity for a different diameter can be calculated using:

Velocity2 = Velocity1 (Diameter1 / Diameter2)2

where,

Velocity = (Flow) / (Free area)

Conservation of mass is often referred to as "conservation of flow," which is confusing because

of the change of flow that can result from change in pressure and temperature (air density).

Only the best commercially available computer programs such as T-Duct (1994) can perform

mass rate balancing instead of flow balancing. These programs will show that volume air-flow

rates at the fan suction and the fan discharge are not equal because of the pressure andtemperature differences, but the mass flow rate is constant.

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 offitting 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 is a measure of the potential energy of a unit of air in the particular crosssection 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.

Dynamic (velocity) pressure is the kinetic energy of a unit of air flow in an air stream.

Dynamic pressure is a funct ion of both air velocity and density:

Dynamic pressure = (Density)x(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, the sum of static and dynamic pressures in a particular duct cross section, is:

Total pressure = (Static pressure) + (Dynamic pressure)

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 (Williams, 1995):

Only total pressure in ductwork always drops in the direct ion of flow. Static or dynamic


2/4

1/9/12


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 incorrect.

The law of energy conservationstates 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 flowstream, 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 momentumis based on Newton's law that a body will maintain its state of restor 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.

As mentioned above, pressure loss in ductwork has two components, frictional losses along duct

walls and dynamic losses in fittings and duct-mounted equipment.

Frictional lossesin duct sections are result from air viscosity and momentum exchange among

particles moving with different velocities. Frictional losses are calculated using theDarcy

equation:

Frictional loss =

where Friction Factordepends on: duct surface roughness; duct diameter; joint type and

spacing; and the Reynolds number, a hydraulic criterion, which specifies the laminar or

turbulent characteristics regime of the air flow.

Air in HVAC ducts generally becomes turbulent where the Reynolds number is larger than 4,000.

There are many formulas for calculating friction factor for turbulent conditions. Colebrook (1938ref168)developed the best-known formula, which requires iterations, in 1938. A simplified

theoretical formula for calculating friction factor in turbulent conditions was developed by Altshul

and modified by Tsal (ASHRAE, 1997). This formula does not require iterat ions.

The easiest way of defining frictional loss per unit length is by using the Friction Chart(ASHRAE,

1997); however, this chart should be used for elevations no higher of 500 m (1,600 ft), air

temperature between 5C and 40C (40F and 100F), and ducts with smooth surfaces. For

different ranges and/or greater accuracy, use the Altshul-Tsal equation.

Dynamic lossesare 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 arereorganized 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 f itting. 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.

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.
http://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htm


3/4



A large number of tables, charts, and formulas are used to calculate local loss coefficients

[Brooks, 1993]. The most advanced work in developing and collecting C-coefficients was done by

Idelchik and Steinberg (1994) ref184.A Computer Duct Fitting Database (DFDB) was developed

by ASHRAE in 1993 (ASHRAE, 1994). The DFDB includes 228 fittings organized by fitting function

(supply, exhaust, common), duct shape (round, rectangular, flat oval), and category (entries,

exits, elbows, transitions, junctions, obstruct ions, fan and system interactions, dampers, hoods,

and duct-mounted equipment).

Pressure loss in a duct section is calculated as the sum of frict ional and dynamic losses using the

Darcy-Weisbachequation:

Pressure loss = ( Frictional loss + C ) (Dynamic pressure)

where, C is the sum of all C-coefficients for fitt ings and duct-mounted equipment in a single

duct. A single duct that has the same shape, cross section, and mass flow is called a duct

sectionor just asection.

For ducts with shapes that are not round, an equivalent diameter is used to calculate pressure

loss. The three types of equivalent diameters are "by friction," "by velocity," and "by flow."

Dynamic pressure must be calculated using air velocity based on the equivalent by-velocity

diameter, and friction loss must be calculated using the equivalent by-friction diameter. For non-

round ducts, the Darcy-Weisbach equation should be used instead of the frict ion chart, andequivalent by-friction diameter should be calculated using what is called the hydraulic diameter,

which applies to any duct shape. It is calculated as:

Hydraulic diameter = 4 (Free area) / (Perimeter)

In general, the function between pressure loss and flow can be represented by the following

parabola:

Pressure loss = (Hydraulic constant) (Flow)2

where "Hydraulic constant" depends on duct shape, size, length, material, air density, and the

sum of C-coefficients. All of these variables are presented in the previous equations above.

A similar function between pressure loss and diameter holds true for round ducts where the

pressure loss can be approximated by the following equation:

Pressure loss = (Constant) (Diameter)n

where,

n = between 4 and 5.

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

section:

Gather input data: air flow, duct shape, duct size, roughness, altitude, air temperature,

and fittings;

Calculate air density as a function of altitude and temperature;

Calculate air velocity as a function of air flow and cross section;

Calculate the Reynolds number;

Calculate friction factor using the Altshul-Tsal equation as a function of duct surfaceroughness and Reynolds number;

Calculate local C-coefficients for each fitting used; and

Calculate pressure loss using the Darcy-Weisbach equation.

An excellent way to analyze the hydraulics of a ductwork system is to utilize pressuregradient

diagrams to show the pressure-loss characteristics of the system in the design phase [Graham,1966]. The diagram will also pinpoint critical factors when a system is not operating properly.
http://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/references.distributionsystems.htm


4/4


http://ateam.lbl.gov/Design-Guide/DGHtm/laboratoryductdesignprinciples.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/automaticcontrols.htmhttp://ateam.lbl.gov/Design-Guide/DGHtm/helpcontents1.htmhttp://ateam.lbl.gov/Design-Guide/DGToc.htm

Basic Duct Hydraulics

Documents

Transcript of Basic Duct Hydraulics