Part 44 (1/2)

[Illustration: Bankers Trust Building, New York City, Operation 900 Horse Power of Babcock & Wilcox Boilers]

FLOW OF STEAM THROUGH PIPES AND ORIFICES

Various forh pipes have been advanced, all having their basis upon Bernoulli's theoreh circular pipes with the proper modifications made for the variation in constants between steaiven by Unwin (based upon Weisbach) as

f 2 v W L E_{f} = ---------- (37) gd

where E is the energy loss in foot pounds due to the friction of W units of weight of steah a pipe d feet in diaravity (322) and f the coefficient of friction

Nuiven for this coefficient of friction, f, which, from experiment, apparently varies with both the dia steam There is no authentic data on the rate of this variation with velocity and, as in all experie of velocity has seemed less than the unavoidable errors of observation, the coefficient is assumed to vary only with the size of the pipe

Unwin established a relation for this coefficient for steam at a velocity of 100 feet per second,

/ 3 f = K| 1 + --- | (38) 10d /

where K is a constant experimentally determined, and d the internal diameter of the pipe in feet

If h represents the loss of head in feet, then

f 2 v W L E_{f} = Wh = ---------- (39) gd

f 2 v L and h = -------- (40) gd

If D represents the density of the steaht per cubic foot, and p the loss of pressure due to friction in pounds per square inch, then

hD p = --- (41) 144

and from equations (38), (40) and (41),

D v L / 3 p = -------- K | 1 + --- | (42) 72 g d 10d /

To convert the velocity term and to reduce to units ordinarily used, let d_{1} the diameter of pipe in inches = 12d, and w = the flow in pounds per minute; then

[pi] / d_{1} w = 60v --- | ---- |{2} D 4 12 /

96 w and v = -------------- [pi] d_{1}2 D

Substituting this value and that of d in formula (42)

/ 36 w{2} L p = 004839 K | 1 + ----- | ----------- (43) d_{1} / D d_{1}{5}

Some of the experimental determinations for the value of K are: K = 005 for water (Unwin)

K = 005 for air (Arson)

K = 0028 for air (St Gothard tunnel experiments)