HVAC Tutorial Overview
A force is required to accelerate a fluid through a
duct system and overcome opposing forces from the
system. On entering a system, fluid accelerates from
zero velocity in the surrounding atmosphere to the
system inlet velocity. When the fluid is expelled
from the system, it decelerates from the system
discharge velocity to zero velocity in the
surrounding atmosphere. Between the system inlet and
discharge, the fluid will accelerate and decelerate
at each change in duct cross sectional area.
Finally, as the fluid flows through the system it
rubs against the system walls and fittings which
impede the flow  the system supplies a force in
opposite direction of flow.
In a duct system, a fan is used to
supply the necessary forces to bring the fluid from
rest to the system velocity and overcome friction
forces. The force exerted by the fan is the fan
total force; or in terms of pressure, the fan total
pressure. The total pressure is divided into two
vector components. The first component, velocity
pressure, is in the direction of flow and whose
magnitude is positive and proportional to the
velocity. The second component, normal to the
direction of flow, is the static pressure. Static
pressure may be positive, exerting outward from the
frame of reference, or negative, exerting inward.
Velocity pressure is always positive, and the sum of
static and velocity pressure is the total pressure.
System Resistance
When a fluid flows through a system it encounters
resistance due to friction and dynamic losses.
Friction losses, as the name suggests, are due to
the fluid rubbing against the walls of the system.
The loss is dependent on the size and shape of the
duct, the duct material, the fluid viscosity, and
the fluid velocity. Dynamic losses include: shock,
heat, and any other losses due to the conversion of
energy. Dynamic losses are dependent on the size and
shape of the duct, the fluid viscosity, and the
fluid velocity. The sum of both friction and dynamic
losses combine to form the total loss of mechanical
energy due to resistance.
The total of all pressure losses in
a system must be overcome by expending energy from
an external force. This is usually done with a fan
which delivers air at a pressure large enough to
overcome all system resistances. A fan should be
selected with a rating high enough to pull the air
into the system (exhaust fans) or push the air out
of the system (supply fans) and overcome all system
resistance. The energy required to pull the air into
and push it out of the system is discussed below
under Entry and Exit Conditions.
The sum of pressure losses in each
component in the system is the total system loss.
This includes straight duct sections, elbows,
transitions, filters, static regain, entry and exit
losses, etc. However, in multiple branch systems,
only the path with the largest pressure loss should
be considered. This is because the pressure at any
junction is equal at the leg of both branches, and
therefore the pressure drop in all branches will
ultimately be equal. Finally, when selecting a
branch, the velocity pressure lost at the system
discharge must also be considered.
Conservation of Energy
The laws of conservation of energy state that energy
is always conserved in one form or another. In the
case of a fluid system, the total pressure at any
two points will be equal with exception to the
energy that is dissipated through heat, sound, and
shock. The dissipated energy is a loss in useful
mechanical energy to the system – it is converted to
a form which cannot be regained by the system.
Therefore, the equation relating two points in a
system is:
Total Pressure at A = Total Pressure at B + System
Losses
Since
total pressure is the sum of velocity pressure and
static pressure:
Static Pressure at A + Velocity Pressure at A =
Static Pressure at B + Velocity Pressure at B +
System Losses
Velocity Pressure
Velocity pressure is the component of total pressure
in the direction of flow and whose magnitude is
positive and proportional to the velocity. The
velocity pressure is equal to the kinetic energy of
the fluid in terms of head. The units of kinetic
energy, like potential energy, are feet of head of
that fluid. In HVAC applications it is customary to
convert this to inches of water. Following is the
derivation of velocity pressure for a fluid in terms
of inches of water.
Pv = (rgas
/
rh2o)
* v^2 / 2g 

=
rgas
* v^2 / (rh2o *
2g) 
Rearrange 
=
rgas
* v^2 / (rh2o *
2 * 32.174 * 60^2) 
Substitute g and convert to
ft/min^2 
=
rgas
* v^2 / (5.193 * 64.348 * 60^2) 
Substitute density of H2o 
=
rgas
* v^2 / (334.159 * 60^2) 
Combine terms 
=
rgas
* v^2 / (18.28^2 * 60^2) 
Rewrite term as squared 
=
rgas
* v^2 / (1097^2) 
Combine terms 
=
rgas
* (v / 1097)^2 
Combine again 
Derivation of velocity pressure equation
Example:
Given a 30 inch diameter duct with
10,000 CFM of standard air, find the velocity
pressure.
Pv = 0.075 (2037 /
1097)^2 = 0.258 inches of water
Static Pressure
Static pressure is the component of total pressure
normal to the direction of flow and is equal to
total pressure minus velocity pressure. Static
pressure may be positive, exerting outward from the
frame of reference, or negative, exerting inward.
Entry Conditions
On entering a duct system, the air accelerates from
zero velocity in the surrounding atmosphere to the
duct velocity. This process involves the
transformation of pressure energy into kinetic
energy, which means that, as the velocity pressure
goes up, the static pressure will go down. In
addition to the transformation of energy, there will
be a pressure loss whose magnitude depends on the
configuration of the entrance fitting; this loss
will decrease the total pressure. If the surrounding
atmospheric pressure is taken to be zero, the
velocity pressure in the duct will be positive, the
static pressure will be negative, and the total
pressure will fall between them. In this case the
static pressure is referred to as the static suction
and is measured near the entrance of the hood.
The total pressure loss on entering
the duct system is the sum of two components: the
transformation of energy from pressure to kinetic,
sometimes referred to as acceleration loss, and the
pressure loss due to the entry fitting. Since the
acceleration loss involves the transformation of
zero velocity pressure in the surrounding atmosphere
to the velocity pressure in the system, it is equal
to the velocity pressure in the system. The other
component is the hood loss and is equal to a loss
coefficient times the velocity pressure just past
the hood.
The pressure loss Pl and static suction Psuction
in the duct can be determined by:
Pl =
Kl
PV1
Psuction =
Pv1 /
Ke^2
Pl is the pressure
loss in the duct element
Psuction is the
static pressure at the duct entrance
Kl is the loss
coefficient (see tables below)
Ke is the coefficient
of entry (see tables below)
Pv1 is the
velocity pressure at point 1 (depicted in the figure
below)
Kl =
0.90 
Kl =
0.50 
Kl =
0.05 
Kl =
0.05 
See Table Below 
Ke =
0.73 
Ke =
0.82 
Ke =
0.98 
Ke =
0.98 
See Table Below 
Coefficients for Entry Conditions
The table below depicts coefficients
for the converging taper where the total included
angle between the sides of the hood is shown in the
Angle column – in degrees. The coefficients are
approximate and include both round and rectangular
ductwork.
q
(degrees) 
KL 
KE 
20 
0.10 
0.95 
40 
0.05 
0.98 
60 
0.10 
0.95 
80 
0.15 
0.94 
100 
0.20 
0.92 
120 
0.25 
0.90 
140 
0.30 
0.86 
160 
0.35 
0.84 
180 
0.40 
0.80 
Converging Duct Coefficients
When a fan is located at the
entrance of a duct system, the entrance losses
become part of the fan work and should not be added
to the system pressure losses. However, when this is
not the case, entrance losses must be added.
For example:
·
entrance losses on a
supply fan without inlet ductwork should not be
calculated
·
entrance losses on an
exhaust fan where the system is connected to the fan
inlet must be calculated
Example:
Given a BellMouthed entry to a 30
inch diameter duct with 10,000 CFM of standard air,
find:
1.
The entry loss
2.
The static suction
From the velocity pressure example
and the tables above:
Pv = 0.258 w.g.,
Kl
= 0.05 and
Ke = 0.98
1.
Pl
= Kl
Pv = 0.05 (0.258) = 0.0129 w.g.
2.
Psuction
= Pv
/ Ke^2
= 0.258 / 0.98^2 = 0.269 w.g.
Therefore, if the hood were part of
an exhaust system, the total pressure loss would be
equal to the entry loss 0.0129 w.g. plus the
velocity pressure (acceleration loss) 0.258 w.g. or
0.271 inches of water.
Exit Conditions
On exiting from a duct system, the air decelerates
from the duct velocity to zero velocity in the
surrounding atmosphere. This process involves
dissipation of the kinetic energy of the air stream.
The static pressure in the stream will be equal to
the surrounding atmospheric pressure. If the
atmospheric pressure is taken to be zero, the total
pressure at the exit will equal the velocity
pressure at the exit, and the exit loss will also
equal the velocity pressure.
Pl =
Pv1
Pstatic =
Pv1
Straight Ducts
The resistance to flow through a straight duct can
be determined using the velocity pressure
Pv, the
duct length
L, the Darcy
friction factor
f, and the
equivalent diameter
D.
Pl
= f Pv L / D
Elbows
The resistance to flow through elbows and bends can
be determined with the velocity pressure
Pv, and a loss
coefficient for the elbow.
Pl =
Kl
Pv
The loss coefficient is dependent
upon the whether the elbow is round, square, or
rectangular; the angle of the elbows bend; the curve
ratio; and to some degree the aspect ratio if the
elbow is rectangular. The curve ratio is the inside
radius divided by the outside radius. The aspect
ratio is the depth along the axis of the bend,
divided by the width in the plane of the bend.
AR = D / W
CR = R1
/ R2
For an
elbow with throat radius
R1 equal to the duct
width
W:
Rcl
= 3/2 W, R1 = W, and R2 = 2W
CR = 1/2
For an elbow with throat radius
R1
equal to
1/2
the duct width
W:
Rcl
= W, R1 = 1/2 W, and R2 3/2 W
CR = 1/3
Note that both the radius ratio, and
curve ratio are directly proportional to the throat
radius.
Rectangular
Duct 

Round
Duct 

Angle
Factors 

AR
Factors 
CR 
Kl 

CR 
Kl 

Angle 
Factor 

AR 
Factor 
Miter 
1.50 

Miter 
1.50 

30 
0.4 

0.2 
2.1 
0.1 
0.60 

0.1 
0.70 

60 
0.7 

0.4 
1.6 
0.2 
0.35 

0.2 
0.50 

90 
1.0 

0.6 
1.2 
0.3 
0.25 

0.3 
0.40 

120 
1.2 

0.8 
1.1 
0.4 
0.18 

0.4 
0.30 

150 
1.4 

1 to 2.5 
1.0 
0.5 
0.15 

0.5 
0.28 

180 
1.5 

3.0 
1.0 
0.6 
0.12 

0.6 
0.24 




3.5 
0.9 
0.7 
0.11 

0.7 
0.24 




4.0 
0.8 
Elbow Loss Coefficients and Correction Factors
The tables above give the pressure
loss coefficients for various curve ratios; angle of
bend and aspect ratio factors. The first two tables
list coefficients for various curve ratios, the
third lists angle of bend factors, and the last is
an aspect ratio factor table.
The angle of bend factor must be
multiplied by the loss coefficient for any elbow
with an angle that is not 90 degrees. The last table
is an aspect ratio table; these factors must be
multiplied by the loss coefficient for rectangular
duct whose aspect ratio is not with the range 1.0 to
2.5.
Finally, as a rule of thumb in the
region of 0.5 curve ratio (1 1/2 centerline radius),
the equivalent length of straight duct for a 90
degree round elbow is about 9 to 10 diameters.
Similarly, the equivalent length of a 90 degree
rectangular elbow is about 6 to 8 equivalent
diameters.
Example:
Given a 30 inch diameter 45 degree
elbow with 10,000 CFM of standard air, and a 30 inch
throat radius, find the pressure loss in the duct.
From the velocity pressure example
and the tables above
Pv = 0.258 w.g.
CR
= 0.50
Kl'
= 0.15
AngleFactor
= 0.55
Kl =
Kl’
AngleFactor =
.0825
Pl =
Kl
Pv = .0825 x 0.258 =
.021
Fan Inlet Pressure
When ductwork is connected to the inlet of a fan,
the fan must generate enough static pressure to pull
the air into the system and reach the velocity
pressure of the fan inlet. Unlike the fan discharge,
it is the static pressure which is responsible for
both pressure losses and velocity. The static
pressure at a fan inlet is negative and has a
magnitude equal to the fan inlet velocity pressure
plus the total resistance to flow through the
system. Also, note that the total pressure prior to
the system entrance is zero, so the system entrance
total pressure minus system losses, is simply the
negative of system losses.
There may be transformations of
pressure energy to velocity energy between these two
points, but the conversions are twofold; energy is
transformed to and from static pressure. Along with
these transformations there will be losses, one
hundred percent regain is impossible, but these are
added to the system loss term.
Fan Inlet Total Pressure =  System Losses
Fan Inlet Static Pressure =  Fan Inlet Velocity
Pressure  System Losses
Fan Outlet Pressure
When ductwork is connected to the outlet of a fan
there are losses associated to the system and the
dissipation of energy at the system discharge. At
the end of the system discharge duct, the static
pressure is zero and therefore the total pressure at
that point is equal to the velocity pressure. Moving
from the system discharge to the fan outlet, the
total pressure rises in proportion to the system
pressure loss. That is, at the fan outlet, the total
pressure is equal to the system discharge total
pressure plus the system losses between the two
points.
Fan Outlet Total Pressure = System Discharge
Velocity Pressure + System Losses
Fan Outlet Static Pressure = System Discharge
Velocity Pressure + System Losses  Fan Outlet
Velocity Pressure
There may be transformations of
pressure energy to velocity energy between these two
points, but the conversions are twofold; energy is
transformed to and from static pressure. Along with
these transformations there will be losses, one
hundred percent regain is impossible, but these are
added to the system loss term.
Fan Inlet and Outlet Pressure
The total energy delivered to a system by a fan is
the fan total pressure. The fan total pressure is
equal to the fan outlet total pressure minus the fan
inlet total pressure. Fan velocity pressure is
defined as the velocity pressure at the fan outlet,
not the change in velocity pressure across the fan.
Finally, fan static pressure, as expected, is equal
to fan total pressure minus fan velocity pressure.
Fan Outlet Total Pressure = System Discharge
Velocity Pressure + Discharge System Losses
Fan Inlet Total Pressure =  Inlet System Losses
Fan Total Pressure = Fan Outlet Total Pressure  Fan
Inlet Total Pressure
Fan Total Pressure = System Discharge Velocity
Pressure + Discharge System Losses  ( Inlet System
Losses)
Fan Total Pressure = System Discharge Velocity
Pressure + Discharge System Losses + Inlet System
Losses
Fan Total Pressure = System Discharge Velocity
Pressure + System Losses
Fan Static Pressure = Fan Total Pressure  Fan
Velocity Pressure
Fan Static Pressure = Fan Total Pressure  Fan
Outlet Velocity Pressure
Fan Static Pressure = System Discharge Velocity
Pressure  Fan Outlet Velocity Pressure + System
Losses
There are several important points
to remember:
1.
The fan velocity
pressure is not the change in velocity pressure
across the fan, it is equal to the fan discharge
velocity pressure
2.
The system loss term
includes the entry loss which is a function of the
entry fitting and the velocity pressure at that
fitting  do not add a kinetic energy term to this
loss. The kinetic energy term is always taken into
account at the system exit.
3.
On a fan with an inlet
duct and an open outlet, the system discharge and
fan outlet are the same. Therefore the fan static
pressure is equal only to the system losses.
4.
These equations are
correct for all fans, with and without inlet and or
outlet ductwork.
Fan Rating
Fan rating catalogs are in terms of Fan Total
Pressure or Fan Static Pressure. Fan total pressure
is the increase in pressure across the fan, and fan
static pressure is the fan total pressure minus the
fan velocity pressure (as described above). When
selecting a fan from a catalog, care should be taken
to determine the ratings, which are usually in terms
of fan static pressure.
Finally, note the chart rating
temperature and fluid density. Usually the charts
list ratings based on air at 70 degrees F and 0.075
lb. per cubic foot. If this is not the case, the
pressures must be corrected for the desired
temperature. This can be done by multiplying by the
ratio of densities. If the fluid temperature is
higher than standard, its density will be smaller,
and its pressure loss will also be smaller.
Absolute Roughness
Absolute roughness
e, is a measure of how
rough a surface is. All surfaces have high and low
points, and the average distance between these is
the absolute roughness. Relative roughness is the
absolute roughness divided by the effective
diameter.
The absolute roughness of a pipe or
duct section in which a fluid flows is directly
proportional to the pressure losses: the larger the
absolute roughness, the larger the pressure losses
in a system.
For example, if you were to push an
object across a polished tile floor, it would slide
with very little resistance (small absolute
roughness). However, if the same objects were pushed
across a concrete floor, the floor would offer
greater resistance and the object would be harder to
push (large absolute roughness).
Condition 
Typical Surface 
Average 
Low 
High 
Very Smooth 
Drawn Tubing 
0.000005 
 
 
Medium Smooth 
Aluminum Duct 
0.00015 
0.0001 
0.0002 
Average 
Galvanized Duct 
0.0005 
0.00045 
0.00065 
Medium Rough 
Concrete Pipe 
0.003 
0.001 
0.01 
Very Rough 
Riveted Steel 
0.01 
0.003 
0.03 
Absolute Roughness Values in feet
Equivalent diameter and hydraulic radius
To aid in calculations on round and rectangular
ductwork, the concept of hydraulic radius and
equivalent diameter is used. The hydraulic radius is
the crosssectional area divided by the perimeter,
and the equivalent diameter is 4 times the hydraulic
radius.
Round Duct 
Rectangular Duct 
Symbols 

A =
p
r2 
A = x y 
A  Area 
S  Perimeter 
S = 2p
r 
S = 2 (x + y) 
D  Diameter 
R  Radius 
Re
= A/S = r/2 
Re
= A/S = x y / (2 (x + y)) 
X  Width 
Y  Height 
De
= 4 Re
= D 
De
= 4 Re
= 2 x y / (x + y) 
Re
 Hydraulic rad. 
De
– Equiv. dia. 
Derivation of Equivalent Diameter
Kinematic Viscosity
Viscosity is a measure of resistance of a fluid to
flow. This resistance acts against the motion of any
solid object through the fluid, against the motion
of the fluid through any stationary object, and
internally within the fluid between slower and
faster moving adjacent layers. A fluid is said to be
viscous if it has a relatively high resistance to
flow, such as molasses. All fluids exhibit viscosity
to some degree.
Mathematically, dynamic or absolute
viscosity
m
is the proportionality factor relating sheer stress
t
to velocity gradient
du/dy.
Kinematic viscosity
n is the absolute
viscosity divided by the mass density of the fluid
r.
t
=
m
du/dy
n =
m
/
r
The viscosity of a fluid is directly
proportional to the pressure losses in a system. The
larger the viscosity, the larger the pressure losses
will be.
For example, when a fluid flows
through a system it resists the flow against the
boundaries and against layers of itself. If the
fluid were molasses which has a large viscosity, it
would resist the flow. However, if it was air,
relatively small viscosity, the resistance would not
be as large.
Temperature (F) 
Kinematic
Viscosity ft2/s 
40 
0.00015 
60 
0.00016 
80 
0.00017 
200 
0.00024 
300 
0.00031 
500 
0.00045 
1000 
0.0009 
Viscosity for air at one atmosphere in ft2/s
Darcy Friction Factor
The Darcy friction factor
f,
is a coefficient that relates pressure loss to
pressure velocity, duct length, and an equivalent
duct diameter. There are many equations for various
flow conditions but the most common for HVAC
applications is the Colebrook equation. This
equation is dependent on the duct absolute roughness
e,
the equivalent diameter
D,
and the Reynolds number
Re.
1 / f’ = 2 log (e / (3.7
D) + 2.51 / (Re
f’))
f’
 square root of the friction factor
e

absolute roughness of the ductwork
D

equivalent diameter of the ductwork
Re

Reynolds number for the flow
The Reynolds number
Re, is the ratio of
the inertia force to the shearing force acting on an
element of fluid at a given point. For pipe and
ductwork, it is the diameter times the velocity of
the fluid divided by the kinematic viscosity of the
fluid.
Re
= D V /
n 