Page 657 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

610 A-22.
Miscellaneous Formulas
( Courtesy of Chicago Bridge and Iron Co.)
1. Area of Roofs. 7. Heads for Horizontal Cylindrical Tanks:
Umbrella Roofs: Hemi-ellipsoidal Heads have an ellipsoidal cross section, usually
D = diameter of tank in feet. with minor axis equal to one half the major axis-that is, depth
= � D, or more.
Surface area in } { = 0.842 D 2 ( when radius = diameter)
square feet = 0.882 D" (when radius= 0.8 diameter) Dished or Basket Heads consist of a spherical segment nor-
mally dished to a radius equal to the inside diameter of the
Conical Roofs: tank cylinder (or within a range of 6 inches plus or minus)
Surface area in} { = 0.787 o• (when pitch is% in 12) and connected to the straight cylindrical flange by a "knuckle"
square feet = 0.792 o• (when pitch is lY:i in 12) whose inside radius is usually not less than 6 per cent of the
inside diameter of the cylinder nor less than 3 times the thick-
2. Average weights. ness of the head plate. Basket heads closely approximate hemi-
ellipsoidal heads.
Steel -490 pounds per cubic foot-specific gravity 7.85
Wrought iron -485 pounds per cubic foot-specific gravity 7.77 Bumped Heads consist of a spherical segment joining the
tank cylinder directly without the transition "knuckle." The
Cast iron --450 pounds per cubic foot-specific gravity 7.21 radius = D, or less. This type of head is used only for pressures
l cubic foot air or gas at 32° F., 760 m.m. barometer = mole- of 10 pounds per square inch or less, excepting where a com-
cular weight x 0.0027855 pounds. pression ring is placed at the junction of head and shell.
Sur/ace Area of Heads:
3. Expansion in steel pipe = 0.78 inch per 100 lineal
feet per 100 degrees Fahr. change in temperature = (7a) Hemi-ellipsoidal Heads:
0
0.412 inch per mile per degree Fahr. temperature S =,.. R [l + K (2-K) J
2
change. S = surface area in square feet
R = radius of cylinder in feet
4. Linear coefficients of expansion per degree increase K = ratio of the depth of the head (not including the
in temperature: straight flange) to the radius of the cylinder
Per Degree Per Degree The above formula is not exact but is within limits of
practical accuracy.
Fahrenheit Centigrade
STRUCTURAL STEEL-A-7 (7b) Dished or Basket Heads:
70° to 200° F 0.0000067 Formula (7a) gives surface area within practical limits.
21.1 ° lo 93° C . 0.0000121 (7c) Bumped Heads:
STAINLESS STEEL· TYPE 304 S = ,.. R' (1 + K")
32° to 932° F 0.0000102 S, R, and K as in formula (7a)
0° lo 500° C. . 0.0000184
ALUMINUM Volume of Heads:
-76° to 68° F 0.0000120
-60° to 20° C. . 0.0000216 ( 7 d) Hemi-ellipsoidal Heads:
V =%,..KR"
5. To determine the net thickness of shells for horizontal R = radius of cylinder in feet
cylindrical pressure tanks: K = ratio of the depth of the head ( not including the
straight flange) to the radius of the cylinder
T= 6PD
s (7e) Dished or Basket Heads:
P = working pressure in pounds per square inch Formula (7d) gives volume within practical limits.
D = diameter of cylinder in feet (70 Bumped Heads:
V = Y:l ,.. K R' (1 + Ifs K 2)
S = allowable unit working stress in pounds per square inch V, Kand R as in formula (7d)
T = Net thickness in inches Note: K in above formulas may be determined as follows:
Resulting net thickness must be corrected to gross or actual Herni-ellipsoidal heads-K is known
thickness by dividing by joint efficiency.
Dished Heads-K = M- \I (M-1) (M + l - 2m)
Bumped Heads- K = [M- V M"-1]
6. To determine the net thickness of heads for cylindrical
pressure tanks: MR = principal radius of head in feet
mR = radius of knuckle in feet
(6a) Ellipsoidal or Bumped Heads: R = radius of cylinder in feet
T= 6PD M= MR m=mR
s R R
T, P and D as in formula 5 For bumped heads m = o
(6b) Dished or Basket Heads:
T = 10.6P(MR) 8. Total volume or length of shell in cylindrical tank
s with ellipsiodal or hemispherical heads:
T, S and P as in formula 5 V = Total volume
MR = principal radius of head in feet L = Length of cylindrical c
Resulting net thickness of heads is both net and gross thick- shell I I )IT
O
_
ness if one piece seamless heads are used, otherwise net thick- KD = Depth of head .....___- -
I
ness must be corrected to gross thickness as above. v = ,.. D' KD)icol �
Formulas 5 and 6 must often be modified to comply with -4- (L + 1\1:i
various engineering codes, and state and municipal regulations. .,,.oz
Calculated gross plate thicknesses are sometimes arbitrarily L= (V7-) -1\l;iKD
increased to provide an additional allowance for corrosion. 4