Handbook of air conditioning and refrigeration / Shan K

17.2 CHAPTER SEVENTEEN
17.1 BASICS OF AIRFLOW IN DUCTS
Bernoulli Equation
The Bernoulli equation relates the mean velocity v, in ft/s (m/s), the pressure p, in lb f/ft 2 absolute
(abs.) or psia (Pa abs.), and the elevation z, in ft (m), of a frictionless or ideal fluid at steady state.
When a fluid motion is said to be in steady state, the variables of the fluid at any point along the
fluid flow do not vary with time. Assuming constant density, the Bernoulli equation can be
expressed in the following form:
where p � static pressure, lb f/ft 2 abs. (Pa abs.)
� � fluid density, lb m/ft 3 (kg/m 3 )
g � gravitational acceleration, ft/s 2 (m/s 2 )
g c � dimensional constant, 32.2 lb m� ft/lb f�s 2 (1)
For convenience, lb � lb m (mass).
Steady Flow Energy Equation
(17.1)
For a real fluid flowing between two cross sections in an air duct, pipe, or conduit, energy loss is inevitable
because of the viscosity of the fluid, the presence of the mechanical friction, and eddies.
The energy used to overcome these losses is usually transformed to heat energy. If we ignore the
kinetic energy difference between the value calculated by the mean velocity of the cross section and
the value calculated according to the velocity distribution of the cross section, then the steady flow
energy equation for a unit mass of real fluid is given as
p� 1
� 1
where u � internal energy, Btu/lb (J/kg)
J � Joule’s equivalent, 778 ft� lb f/Btu (1)
q � heat supplied, Btu/lb (J/kg)
W � work developed, ft� lb f/lb (J/s)
(17.2)
In Eq. (17.2), subscripts 1 and 2 indicate the cross section 1 and 2, respectively, and p 1� and p 2�
denote the absolute static pressure at cross section 1 and 2. Signs of q and W follow the convention
in thermodynamics, i.e., when heat is supplied to the system, q is positive and when heat is released
from the system, q is negative. When work is developed by the system, W is positive; and for work
input to the system, W is negative.
Multiply both sides of Eq. (17.2) by �, ignore the difference in densities, and rearrange the
terms. Then each term has the unit of pressure, in lb f/ft 2 abs. (Pa abs.), or
p� 1 � � 1v 1 2
� u 1J � v 1 2
2g c
2g c
� � 1gz 1
g c
p
�
� v2
2g c
� gz 1
g c
� p� 2 � � 2v 2 2
� qJ � p� 2
r 2
2g c
� gz
g c
� constant
� � 2gz 2
g c
� u 2J � v 2 2
� �W � �J(u 2 � u 1 � q)
(17.3)
For an air duct or piping work without a fan, compressor, and pump, �W � 0.
Let the pressure loss from viscosity, friction, and eddies between cross sections 1 and 2 be
�p f � �J(u 2 � u 1 � q); then each term of Eq. (17.3) can be expressed in the form of pressure
2g c
� gz 2
g c
� W