Document 3N093L8rpd006oR0v6Yy51bBn
698
CHAPTER 32
1953 Guide
where
he = pressure loss due to sudden contraction, feet of fluid flowing. - Vs = the velocity at the vena contracta, feet per second. , A'i = the area of the vena contracta, square feet.
Introduction of the contraction coefficient a
Ai A1
and
the
loss
coefficient
^ in Equation 8 gives (with X i = Ai X vj:
or for standard air:
A C. =
Vj-
. 2g
(9)
1 : " - (.y
where
Hc = pressure loss due to sudden contraction, inches of water. Ei -- velocity of standard air in the inlet duct, in feet per minute. .
Values of a and C for sharp corners for increasing ratios of Ai/Al are given in the following table
AiJAi ,
a
c
o.oi 0.1 0.2' 0.4 0.6 0.8 1.00
0.6 0.61 0.62 0.65 0.7 0.7.7 . 1.00 0.44 0.41 0.37 0.29 0.19 0.09 0.00
For discharge to atmosphere from a pipe, C = 1.6 in Equation 10. For a gradual enlargement, Equation 7 changes to
where ff,e = pressure, loss due to gradual enlargement, based on standard air, inches of water. Ci = coefficient of loss, dependent upon the total angle included Between the sides of the duct.
Values for Ci are given in the following table:
Total Included Angle, Degrees
Ci
0
0.20
7 0.15
10,
0.16
20
0.35
30
0.65
40
0.80
50
0.92
60
1.0
Air Duct Design
699
Pressure losses for various duct transitions, and area changes havebeeh
determined experimentally, although the available information is generally restricted to symmetrical area.changes,*7-.14, ,5-16>1!
PRESSURE CHANGES
1 The fundamental energy equation for standard air Sow in a horizontal duct can be written18
+ Loss of pressure (head), inches of water (12)
where
Hi and H, -- the static pressure (head) at two given points (1) and (2), inches
of water.
...
the velocity pressure (head) at the same points, inches of water.
Equation 12 states that the mechanical energy at a given point (1) must be equal to the mechanical energy at another point (2), plus any dissipa tion of mechanical energy to internal energy (loss of ; pressure). Equa tion 12 is valid only if no work is done by or upon the air between the sections (1) and (2), and if there is no heat transfer to or from the air.
( Vy In Equation 12, H is a measure of the potential energy and l 4005 / a
measure of the kinetic energy or energy of motion. The sum of static pressure and velocity pressure is called total pressure, and is a measure of the total energy.
Static pressure and velocity pressure are mutually convertible, that is to say, static pressure may be converted into velocity pressure, and vice versa. Every change in the cross-sectional area of a duct results in such a conversion of energy and is always accompanied by some loss in effi ciency, or loss in total pressure.'
In the final analysis-of pressure losses in ducts, dynamic losses are due to accelerations and decelerations of the air stream as a whole. In a con verging duct, the air velocity will be accelerated; some pressure head will be converted into velocity pressure. This conversion is generally a stable and efficient process, the energy losses are small, and there is no eddyformation.
In an expanding duct section, on the other hand, the air wall be decel erated and an opposing pressure gradient be required to reduce the velocity. If the angle of divergence is appreciable, the flow becomes unstable, there is danger of separation of the flow from the duct wall, and large energy losses and eddy formation are possible.19
In order to keep losses in an expanding duct section to a minimum and to convert the velocity pressure efficiently into static pressure, the angle of divergence should be kept small.20 Theoretically, it might seem possible to increase the duct area so gradually that the reduction in velocity and accompanying loss of velocity pressure would occur reversibly, and thus permit 100 percent conversion to static pressure. Such an ideal applica tion of the principle of static regain in duct design is, of course, impossible for various reasons21 such as: the necessity of using sections of uniform diameter because of cost, the need for using ducts of dimensions varying in full inches, the changing of duct sizes mainly at branch connections, and