Document rEgReMgaOpnK2xZZOMkRz5bq

HEATING VENTILATING AIR CONDITIONING GUIDE 1941 For all practical purposes, the value of may be taken as a constant regardless of the size of the structure. Hence, in general, the volume. a,,j conseouentlv thn mcf ................................ Fig. 6. Economical Chimney Sizes ^Diameter values also for gas temperatures of 400.000 and 600 F The problem is to deduce an equation for the chimney gas velocity which will result in a combination of a height and a diameter whost product HD will be least. The solution is obtained by equating the pro duct of Equations 6 and 7 to HD, differentiating this product with respect to V and equating the resulting expression to zero. This procedure results in the following expression: )V WTr \2/S BolVe fW' where Ve -- economical chimney gas velocity, feet per second. Equation 9 gives the economical velocity of the chimney gases fo any set of operating conditions, and represents the velocity which wil 174 CHIMNEYS AND DRAFT CALCULATIONS . chimney the size of which will cost less than that of any other tfsU,t 1 determined by any other velocity for the same operating con- si?? as After the value of the economical velocity has been determined, ^^corresponding height and diameter can then be determined from e tions 6 and 7, respectively, and the economical size will then be rfU'ned. Equations 6, 7 and 9 may be simplified considerably for attal operating conditions in an average size steam plant by assuming typical conditions. Average chimney gas temperature, 500 F.............................Tc = 960 Mean atmospheric temperature, 62 F.-------------- T0 = 522 Average coefficient of friction. 0.016-....... J = 0.018 Average chimney gas density, 0.09.--------------------- ,--Wc = 0.09 Sea level elevation, with barometer of 29.92.......... _B0 = 29.92 Substituting these values in Equations 9, 7 and 6, respectively, and reducing, the results are substantially: Ve = 13.71V1/S (10) D = 1.5fV2/s (ID . H = 190Z>r (12) Fig. 6 gives the economical chimney sizes for various amounts of gases flowing and for required draft intensities as computed from Equations 10, 11 and 12. They are based on the operating factors .used in reducing Equations 6, 7 and 9 to their simpler form. The sizes shown by the curves in the chart should be used for general operating conditions only, or for installations where the required data necessary for an exact deter mination are difficult or impossible to secure. Whenever it is possible to secure accurate data, or the anticipated operating conditions are fairly well known, the required size should be determined from Equations 6, 7 and 9. The recommended minimum inside dimensions and heights of chimneys for small and medium size installations are given in Table 1. GENERAL EQUATION The general draft equation for a steam producing plant may be stated as follows: Dt -- hi ~ hp -f Ab 4- had + he + ABr 4- Av + ho + Ae + Ar (13) where Dt = theoretical draft intensity created by pressure transformer, inches of water. hi = draft loss due to friction in pressure transformer, inches of water. Af = draft loss through the fuel bed, inches of water. Ab = draft loss through the boiler and setting, inches of water. ABr = draft loss through the breeching, inches of water. Av = draft loss due to velocity, inches of water. Afid = draft loss due to bends, inches of water. Ac = draft loss due to contraction of opening, inches of water. Ao = draft loss due to enlargement of opening, inches of water. Ae = draft loss through the economizer, inches of water. Ar = draft loss through recuperators, regenerators, or air heaters, inches of water. 175