Part 67

All surfaces should be painted before the covering is applied. Canvas is ordinarily placed over the covering, held in place by wrought-iron or brass bands.

Expansion and Support of Pipe--It is highly important that the piping be so run that there will be no undue strains through the action of expansion. Certain points are usually securely anchored and the expansion of the piping at other points taken care of by providing supports along which the piping will slide or by means of flexible hangers. Where pipe is supported or anchored, it should be from the building structure and not from boilers or prime movers. Where supports are furnished, they should in general be of any of the numerous sliding supports that are available. Expansion is taken care of by such a method of support and by the providing of large radius bends where necessary.

It was formerly believed that piping would actually expand under steam temperatures about one-half the theoretical amount due to the fact that the exterior of the pipe would not reach the full temperature of the steam contained. It would appear, however from recent experiments that such actual expansion will in the case of well-covered pipe be very nearly the theoretical amount. In one case noted, a steam header 293 feet long when heated under a working pressure of 190 pounds, the steam superheated approximately 125 degrees, expanded 8¾ inches; the theoretical amount of expansion under the conditions would be approximately 9-35/64 inches.

FLOW OF STEAM THROUGH PIPES AND ORIFICES

Various formulae for the flow of steam through pipes have been advanced, all having their basis upon Bernoulli's theorem of the flow of water through circular pipes with the proper modifications made for the variation in constants between steam and water. The loss of energy due to friction in a pipe is given by Unwin (based upon Weisbach) as

f 2 v² 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 steam passing with a velocity of v feet per second through a pipe d feet in diameter and L feet long; g represents the acceleration due to gravity (32.2) and f the coefficient of friction.

Numerous values have been given for this coefficient of friction, f, which, from experiment, apparently varies with both the diameter of pipe and the velocity of the passing steam. There is no authentic data on the rate of this variation with velocity and, as in all experiments, the effect of change 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 v² W L E_{f} = Wh = ---------- (39) gd

f 2 v² L and h = -------- (40) gd

If D represents the density of the steam or weight 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 v² 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

/ d_{1}\ w = 60v × --- | ---- |^{2} D 4 \ 12 /

9.6 w and v = -------------- d_{1}^2 D

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

/ 3.6 \ w^{2} L p = 0.04839 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). K = .0026 for steam (Carpenter at Oriskany). K = .0027 for steam (G. H. Babcock).

The value .0027 is apparently the most nearly correct, and substituting in formula (43) gives,

/ 3.6 \ w^{2} L p = 0.000131 | 1 + ---- | ----------- (44) \ d{1}/ D d{1}^{5}

/ pDd{1}^{5} \ w = 87 | -------------- |^{½} (45) | / 3.6 \ | | | 1 + ---- | L | \ \ d{1}/ /

Where w = the weight of steam passing in pounds per minute, p = the difference in pressure between the two ends of the pipe in pounds per square inch, D = density of steam or weight per cubic foot, d_{1} = internal diameter of pipe in inches, L = length of pipe in feet.