Document B5KnBZD35Zdkagyzz5mXQX8d8

664 CHAPTER 31 Values for Ci are given in the following table: . " 1950 Guide Total Included Angle, Degrees 5 c. 0.20 7~ ' 0.15 10 0.16 20 0.35 30 0.65 40 0.80 60 0.92 60 1.0 PRESSURE CHANGES 1 ' The fundamental energy equation for standard air flow in a horizontal duct can be written15 H,+ + Loss of Pressure (head) (12) where H, and H, = the static pressure (head) at two given points (1). and.(2), inches of water. (4005) an<^ (4005) = velocity Preasure (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. only valid, if no work is done by or. upon the air between the sections (i) and (2), and if there is no heat "transfer to or from-the air. In Equation 12, H is a measure of the potential energy and ^4^5) measure of the kinetic energy or energy of motion; The sum of static pressure and velocity pressure is called total (dynamic, impact) 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 transformed into'velocity pressure, and vice versa. Every change in the cross-sectional area of a duct, results in such a conversion of energy, which is always accompanied by some loss in efficiency, or loss in total pressure. In the final analysis of pressure losses in ducts, shock losses are therefore due to accelerations and decelerations of the air stream as a whole. In a converging duct, the air velocity will be accelerated ; some pressure head will be . converted into: velocity pressure.. ..Thip conversion is. generally a Stable and efficient process, the energy losses are small, and there is no eddy formation. In an expanding duct section on the other hand, the air will be decel erated and an opposing pressure gradient is 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 posable.15 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.1? 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 per cent conversion to static pressure. . Such' an.ideal applica tion of the principle of static regain in duct design is, of course, impossible AirCuctDesign 655 for various reasons1* 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 the inevitable loss due to' turbulence. The principle of static pressure regain is, however, of importance in the economical design of duct systems. Fig. 7 shows the application of static pressure regain to a simple fan and discharge duct.1* The fan in the upper part of the figure has a free inlet and discharges air through a straight duct, the diameter of which is equal to the fan outlet. The totalpressure which must be provided by the fan is therefore the sum of the pressure that is necessary to overcome the fric tion in the duct (no shock pressure loss), plus the velocity pressure which in this case is the same at any location along the length of the duct. /X t-- Arrangement A ZZ3 (Velocity/' Pressure ' ; ofthe Air Learing ;) ttie System. ''Atmospheric Pressure Arrangement B After Section '`Expanding Section -jyDecrease in TotalPressure * Oue to Static Pressure Regain ^Atmospheric* Velocity Pressure Ofthe AirLeaving the Systemj . 'Static Pressure Re gainin Expanding Section. Fig. 7. Application op Static Pressure Regain to.a Simple Fan -- and Discharge Duct . In arrangement B in the lower part of Fig. 7, a diverging section, with after section, has been added to the straight duct. The velocity in the diverging section:is therefore decreased; and velocity pressure converted into static'pressure before the1 air is released to the atmosphere. It' cab be seen that in case B, the total pressure at the fan outlet'is less-than in case A; and thqs;a saving in horsepower can be effected.., :: The regain in static pressure h, in. an abruptly expanded section is .the difference in the velocity pressures of the small and the large duct, minus, the shock pressure loss (Equation 6): . ; -r> ' . or simplified K ]-- p,)1 2g (13) Vl(Vl -- Vl) gg (14)