Page 34 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

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Appendix A

COMMONLY USED FORMULAS

A-1. PROPORTION AND RATIO A = πr 2
r = √ A/π
Direct proportion: where
a:b = c:d, or ad = bc C = circumference
d = diameter
Inverse proportion:
r = radius
a:d = b:c, or ac = bd π = 3.1416
where A = area.
a = small, or first term
b = small, or second term Cone, right circular:
c = large, or third term L = ½sC
d = large, or fourth term.
V = ⅓ (BH)
2
Pulley ratio: V = ⅓ (πr h)
where
S /S = d /d A
B
A
B
where L = lateral surface
S = speed of pulley A s = slant height
A
S = speed of pulley B V = volume
B
d = diameter of pulley A B = area of base
A
r = radius of base
d = diameter of pulley B. h = height, or altitude
B
Gear ratio: π = 3.1416
C = circumference of base.
S × T = S × T B
B
A
A
where
S = speed of gear A Cube:
A
T = number of teeth in gear A V = l 3
A
S = speed of gear B where
B
T = number of teeth in gear B. V = volume
B
l = length of one side.
A-2. LENGTH, AREA, AND VOLUME Cylinder, right:
Board feet: L = 2πrh
t × w × l L = hC
bd ft = ———–
12 T = 2πr(r + h)
V = Bh
where
2
bd ft = board feet in lumber V = πr h
t = thickness of board, in inches where
Petroleum Extension-The University of Texas at Austin
w = width of board, in inches L = lateral surface
l = length of board, in feet. T = total surface area
r = radius of base
Circle: h = altitude
C = πd C = circumference of base
C = π2r π = 3.1416
d = C/π V = volume
d = 2r B = area of base.
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