Chapter 39

In practice the limiting factor in the velocity advisable is the allowable pressure drop. In the description of the action of the throttling calorimeter, it has been demonstrated that there is no loss accompanying a drop in pressure, the difference in energy between the higher and lower pressures appearing as heat, which, in the case of steam flowing through a pipe, may evaporate any condensation present or may be radiated from the pipe. A decrease in pipe area decreases the radiating surface of the pipe and thus the possible condensation. As the heat liberated by the pressure drop is utilized in overcoming or diminishing the tendency toward condensation and the heat loss through radiation, the steam as it enters the prime mover will be drier or more highly superheated where high steam velocities are used than where they are lower, and if enough excess pressure is carried at the boilers to maintain the desired pressure at the prime mover, the pressure drop results in an actual saving rather than a loss. The whole is analogous to standard practice in electrical distributing systems where generator voltage is adjusted to suit the loss in the feeder lines.

In modern practice, with superheated steam, velocities of 15,000 feet per minute are not unusual and this figure is very frequently exceeded.

Piping System Design--With the proper size of pipe to be used determined, the most important factor is the provision for the removal of water of condensation that will occur in any system. Such condensation cannot be wholly overcome and if the water of condensation is carried to the prime mover, difficulties will invariably result. Water is practically incompressible and its effect when traveling at high velocities differs little from that of a solid body of equal weight, hence impact against elbows, valves or other obstructions, is the equivalent of a heavy hammer blow that may result in the fracture of the pipe. If there is not sufficient water in the system to produce this result, it will certainly cause knocking and vibration in the pipe, resulting eventually in leaky joints. Where the water reaches the prime mover, its effect will vary from disagreeable knocking to disruption. Too frequently when there are disastrous results from such a cause the boilers are blamed for delivering wet steam when, as a matter of fact, the evil is purely a result of poor piping design, the most common cause of such an action being the pocketing of the water in certain parts of the piping from whence it is carried along in slugs by the steam. The action is particularly severe if steam is admitted to a cold pipe containing water, as the water may then form a partial vacuum by condensing the steam and be projected at a very high velocity through the pipes producing a characteristic sharp metallic knock which often causes bursting of the pipe or fittings. The amount of water present through condensation may be appreciated when it is considered that uncovered 6-inch pipe 150 feet long carrying 3600 pounds of high pressure steam per hour will condense approximately 6 per cent of the total steam carried through radiation. It follows that efficient means of removing condensation water are absolutely imperative and the following suggestions as to such means may be of service:

The pitch of all pipe should be in the direction of the flow of steam. Wherever a rise is necessary, a drain should be installed. All main headers and important branches should end in a drop leg and each such drop leg and any low points in the system should be connected to the drainage pump. A similar connection should be made to every fitting where there is danger of a water pocket.

Branch lines should never be taken from the bottom of a main header but where possible should be taken from the top. Each engine supply pipe should have its own separator placed as near the throttle as possible. Such separators should be drained to the drainage system.

Check valves are frequently placed in drain pipes to prevent steam from entering any portion of the system that may be shut off.

Valves should be so located that they cannot form water pockets when either open or closed. Globe valves will form a water pocket in the piping to which they are connected unless set with the stem horizontal, while gate valves may be set with the spindle vertical or at an angle. Where valves are placed directly on the boiler nozzle, a drain should be provided above them.

High pressure drains should be trapped to both feed heaters and waste headers. Traps and meters should be provided with by-passes. Cylinder drains, heater blow-offs and drains, boiler blow-offs and similar lines should be led to waste. The ends of cylinder drains should not extend below the surface of water, for on starting up or on closing the throttle valve with the drains open, water may be drawn back into the cylinders.

TABLE 64

RADIATION FROM COVERED AND UNCOVERED STEAM PIPES

CALCULATED FOR 160 POUNDS PRESSURE AND 60 DEGREES TEMPERATURE

+---------------------------------------------------------------------+ |+------+---------------------------+----+----+----+-----+-----+-----+| || | | | | | | | || || Pipe | |1/2 |3/4 | 1 |1-1/4|1-1/2| || ||Inches| Thickness of Covering |inch|inch|inch|inch |inch |Bare || |+------+---------------------------+----+----+----+-----+-----+-----+| || |B. t. u. per lineal foot | | | | | | || || | per hour |149 |118 | 99 | 86 | 79 | 597 || || |B. t. u. per square foot | | | | | | || || | per hour |240 |190 |161 | 138 | 127 | 959 || || 2 |B. t. u. per square foot | | | | | | || || | per hour per one degree | | | | | | || || | difference in temperature|.770|.613|.519|.445 |.410 |3.198|| |+------+---------------------------+----+----+----+-----+-----+-----+| || |B. t. u. per lineal foot | | | | | | || || | per hour |247 |193 |160 | 139 | 123 |1085 || || |B. t. u. per square foot | | | | | | || || | per hour |210 |164 |136 | 118 | 104 | 921 || || 4 |B. t. u. per square foot | | | | | | || || | per hour per one degree | | | | | | || || | difference in temperature|.677|.592|.439|.381 |.335 |2.970|| |+------+---------------------------+----+----+----+-----+-----+-----+| || |B. t. u. per lineal foot | | | | | | || || | per hour |352 |269 |221 | 190 | 167 |1555 || || |B. t. u. per square foot | | | | | | || || | per hour |203 |155 |127 | 110 | 96 | 897 || || 6 |B. t. u. per square foot | | | | | | || || | per hour per one degree | | | | | | || || | difference in temperature|.655|.500|.410|.355 |.310 |2.89 || |+------+---------------------------+----+----+----+-----+-----+-----+| || |B. t. u. per lineal foot | | | | | | || || | per hour |443 |337 |276 | 235 | 207 |1994 || || |B. t. u. per square foot | | | | | | || || | per hour |196 |149 |122 | 104 | 92 | 883 || || 8 |B. t. u. per square foot | | | | | | || || | per hour per one degree | | | | | | || || | difference in temperature|.632|.481|.394|.335 |.297 |2.85 || |+------+---------------------------+----+----+----+-----+-----+-----+| || |B. t. u. per lineal foot | | | | | | || || | per hour |549 |416 |337 | 287 | 250 |2468 || || |B. t. u. per square foot | | | | | | || || | per hour |195 |148 |120 | 102 | 89 | 877 || || 10 |B. t. u. per square foot | | | | | | || || | per hour per one degree | | | | | | || || | difference in temperature|.629|.477|.387|.329 |.287 |2.83 || |+------+---------------------------+----+----+----+-----+-----+-----+| +---------------------------------------------------------------------+

Covering--Magnesia, canvas covered.

For calculating radiation for pressure and temperature other than 160 pounds, and 60 degrees, use B. t. u. figures for one degree difference.

Radiation from Pipes--The evils of the presence of condensed steam in piping systems have been thoroughly discussed above and in some of the previous articles. Condensation resulting from radiation, while it cannot be wholly obviated, can, by proper installation, be greatly reduced.

Bare pipe will radiate approximately 3 B. t. u. per hour per square foot of exposed surface per one degree of difference in temperature between the steam contained and the external air. This figure may be reduced to from 0.3 to 0.4 B. t. u. for the same conditions by a 1½ inch insulating covering. Table 64 gives the radiation losses for bare and covered pipes with different thicknesses of magnesia covering.

Many experiments have been made as to the relative efficiencies of different kinds of covering. Table 65 gives some approximately relative figures based on one inch covering from experiments by Paulding, Jacobus, Brill and others.

TABLE 65

APPROXIMATE EFFICIENCIES OF VARIOUS COVERINGS REFERRED TO BARE PIPES +--------------------------------+ |+-------------------+----------+| || Covering |Efficiency|| |+-------------------+----------+| ||Asbestocel | 76.8 || ||Gast's Air Cell | 74.4 || ||Asbesto Sponge Felt| 85.0 || ||Magnesia | 83.5 || ||Asbestos Navy Brand| 82.0 || ||Asbesto Sponge Hair| 86.0 || ||Asbestos Fire Felt | 73.5 || |+-------------------+----------+| +--------------------------------+

Based on one-inch covering.

The following suggestions may be of service:

Exposed radiating surfaces of all pipes, all high pressure steam flanges, valve bodies and fittings, heaters and separators, should be covered with non-conducting material wherever such covering will improve plant economy. All main steam lines, engine and boiler branches, should be covered with 2 inches of 85 per cent carbonate of magnesia or the equivalent. Other lines may be covered with one inch of the same material. All covering should be sectional in form and large surfaces should be covered with blocks, except where such material would be difficult to install, in which case plastic material should be used. In the case of flanges the covering should be tapered back from the flange in order that the bolts may be removed.

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

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

9.6 w and v = -------------- [pi] 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,[80] d_{1} = internal diameter of pipe in inches, L = length of pipe in feet.

TABLE 66

FLOW OF STEAM THROUGH PIPES +---------------------------------------------------------------------------------------+ |Initl|Diameter[81] of Pipe in Inches, Length of Pipe = 240 Diameters | |Gauge|---------------------------------------------------------------------------------+ |Press| ¾ | 1 | 1½ | 2 | 2½ | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 15 | 18 | |Pound|---------------------------------------------------------------------------------+ |/SqIn| Weight of Steam per Minute, in Pounds, With One Pound Loss of Pressure | +-----+---------------------------------------------------------------------------------+ | 1 |1.16|2.07| 5.7|10.27|15.45|25.38| 46.85| 77.3|115.9|211.4| 341.1| 502.4| 804|1177| | 10 |1.44|2.57| 7.1|12.72|19.15|31.45| 58.05| 95.8|143.6|262.0| 422.7| 622.5| 996|1458| | 20 |1.70|3.02| 8.3|14.94|22.49|36.94| 68.20|112.6|168.7|307.8| 496.5| 731.3|1170|1713| | 30 |1.91|3.40| 9.4|16.84|25.35|41.63| 76.84|126.9|190.1|346.8| 559.5| 824.1|1318|1930| | 40 |2.10|3.74|10.3|18.51|27.87|45.77| 84.49|139.5|209.0|381.3| 615.3| 906.0|1450|2122| | 50 |2.27|4.04|11.2|20.01|30.13|49.48| 91.34|150.8|226.0|412.2| 665.0| 979.5|1567|2294| | 60 |2.43|4.32|11.9|21.38|32.19|52.87| 97.60|161.1|241.5|440.5| 710.6|1046.7|1675|2451| | 70 |2.57|4.58|12.6|22.65|34.10|56.00|103.37|170.7|255.8|466.5| 752.7|1108.5|1774|2596| | 80 |2.71|4.82|13.3|23.82|35.87|58.91|108.74|179.5|269.0|490.7| 791.7|1166.1|1866|2731| | 90 |2.83|5.04|13.9|24.92|37.52|61.62|113.74|187.8|281.4|513.3| 828.1|1219.8|1951|2856| | 100 |2.95|5.25|14.5|25.96|39.07|64.18|118.47|195.6|293.1|534.6| 862.6|1270.1|2032|2975| | 120 |3.16|5.63|15.5|27.85|41.93|68.87|127.12|209.9|314.5|573.7| 925.6|1363.3|2181|3193| | 150 |3.45|6.14|17.0|30.37|45.72|75.09|138.61|228.8|343.0|625.5|1009.2|1486.5|2378|3481| +---------------------------------------------------------------------------------------+

This formula is the most generally accepted for the flow of steam in pipes. Table 66 is calculated from this formula and gives the amount of steam passing per minute that will flow through straight smooth pipes having a length of 240 diameters from various initial pressures with one pound difference between the initial and final pressures.

To apply this table for other lengths of pipe and pressure losses other than those assumed, let L = the length and d the diameter of the pipe, both in inches; l, the loss in pounds; Q, the weight under the conditions assumed in the table, and Q_{1}, the weight for the changed conditions.

For any length of pipe, if the weight of steam passing is the same as given in the table, the loss will be,

L l = ---- (46) 240d

If the pipe length is the same as assumed in the table but the loss is different, the quantity of steam passing per minute will be,

Q_{1} = Ql^{½} (47)

For any assumed pipe length and loss of pressure, the weight will be,

/240dl\ Q_{1} = Q|-----|^{½} (48) \ L /

TABLE 67

FLOW OF STEAM THROUGH PIPES LENGTH OF PIPE 1000 FEET

+--------------------------------------------------++----------------------------------------+ | Discharge in Pounds per Minute corresponding to || Drop in Pressure in | | Drop in Pressure on Right for Pipe Diameters || Pounds per Square Inch corresponding | | in Inches in Top Line || to Discharge on Left: Densities | | || and corresponding Absolute Pressures | | || per Square Inch in First Two Lines | +--------------------------------------------------++----------------------------------------+ | Diameter[82]--Discharge || Density--Pressure--Drop | +--------------------------------------------------++----------------------------------------+ | 12 | 10 | 8 | 6 | 4 | 3 | 2½| 2 | 1½| 1 ||.208 |.230|.284|.328|.401|.443|.506|.548| | In | In | In | In | In | In | In | In | In | In || 90 | 100| 125| 150| 180| 200| 230| 250| +--------------------------------------------------++-------+--------------------------------+ |2328|1443| 799| 371|123. |55.9|28.8|18.1|6.81|2.52||18.10|16.4|13.3|11.1|9.39|8.50|7.44|6.87| |2165|1341| 742| 344|114.6|51.9|27.6|16.8|6.52|2.34||15.60|14.1|11.4|9.60|8.09|7.33|6.41|5.92| |1996|1237| 685| 318|106.0|47.9|26.4|15.5|6.24|2.16||13.3 |12.0|9.74|8.18|6.90|6.24|5.47|5.05| |1830|1134| 628| 292| 97.0|43.9|25.2|14.2|5.95|1.98||11.1 |10.0|8.13|6.83|5.76|5.21|4.56|4.21| |1663|1031| 571| 265| 88.2|39.9|24.0|12.9|5.67|1.80|| 9.25|8.36|6.78|5.69|4.80|4.34|3.80|3.51| |1580| 979| 542| 252| 83.8|37.9|22.8|12.3|5.29|1.71|| 8.33|7.53|6.10|5.13|4.32|3.91|3.42|3.16| |1497| 928| 514| 239| 79.4|35.9|21.6|11.6|5.00|1.62|| 7.48|6.76|5.48|4.60|3.88|3.51|3.07|2.84| |1414| 876| 485| 226| 75.0|33.9|20.4|10.9|4.72|1.53|| 6.67|6.03|4.88|4.10|3.46|3.13|2.74|2.53| |1331| 825| 457| 212| 70.6|31.9|19.2|10.3|4.43|1.44|| 5.91|5.35|4.33|3.64|3.07|2.78|2.43|2.24| |1248| 873| 428| 199| 66.2|23.9|18.0|9.68|4.15|1.35|| 5.19|4.69|3.80|3.19|2.69|2.44|2.13|1.97| |1164| 722| 400| 186| 61.7|27.9|16.8|9.03|3.86|1.26|| 4.52|4.09|3.31|2.78|2.34|2.12|1.86|1.72| |1081| 670| 371| 172| 57.3|25.9|15.6|8.38|3.68|1.17|| 3.90|3.53|2.86|2.40|2.02|1.83|1.60|1.48| | 998| 619| 343| 159| 52.9|23.9|14.4|7.74|3.40|1.08|| 3.32|3.00|2.43|2.04|1.72|1.56|1.36|1.26| | 915| 567| 314| 146| 48.5|21.9|13.2|7.10|3.11|0.99|| 2.79|2.52|2.04|1.72|1.45|1.31|1.15|1.06| | 832| 516| 286| 132| 44.1|20.0|12.0|6.45|2.83|0.90|| 2.31|2.09|1.69|1.42|1.20|1.08|.949|.877| | 748| 464| 257| 119| 39.7|18.0|10.8|5.81|2.55|0.81|| 1.87|1.69|1.37|1.15| .97|.878|.769|.710| | 665| 412| 228| 106| 35.3|16.0| 9.6|5.16|2.26|0.72|| 1.47|1.33|1.08|.905|.762|.690|.604|.558| | 582| 361| 200|92.8| 30.9|14.0| 8.4|4.52|1.98|0.63|| 1.13|1.02|.828|.695|.586|.531|.456|.429| +--------------------------------------------------++----------------------------------------+

To get the pressure drop for lengths other than 1000 feet, multiply by lengths in feet ÷ 1000.

Example: Find the weight of steam at 100 pounds initial gauge pressure, which will pass through a 6-inch pipe 720 feet long with a pressure drop of 4 pounds. Under the conditions assumed in the table, 293.1 pounds would flow per minute; hence, Q = 293.1, and

_ _ | 240×6×4 | Q_{1} = 293.1 | ------- |^{½} = 239.9 pounds |_ 720×12_|

Table 67 may be frequently found to be of service in problems involving the flow of steam. This table was calculated by Mr. E. C. Sickles for a pipe 1000 feet long from formula (45), except that from the use of a value of the constant K = .0026 instead of .0027, the constant in the formula becomes 87.45 instead of 87.

In using this table, the pressures and densities to be considered, as given at the top of the right-hand portion, are the mean of the initial and final pressures and densities. Its use is as follows: Assume an allowable drop of pressure through a given length of pipe. From the value as found in the right-hand column under the column of mean pressure, as determined by the initial and final pressures, pass to the left-hand portion of the table along the same line until the quantity is found corresponding to the flow required. The size of the pipe at the head of this column is that which will carry the required amount of steam with the assumed pressure drop.

The table may be used conversely to determine the pressure drop through a pipe of a given diameter delivering a specified amount of steam by passing from the known figure in the left to the column on the right headed by the pressure which is the mean of the initial and final pressures corresponding to the drop found and the actual initial pressure present.