Part 68

TABLE 66

FLOW OF STEAM THROUGH PIPES +---------------------------------------------------------------------------------------+ |Initl|Diameter 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--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.

For a given flow of steam and diameter of pipe, the drop in pressure is proportional to the length and if discharge quantities for other lengths of pipe than 1000 feet are required, they may be found by proportion.

TABLE 68

FLOW OF STEAM INTO THE ATMOSPHERE _________________________________________________________________ | | | | | | | Absolute | Velocity | Actual | Discharge | Horse Power | | Initial | of Outflow | Velocity | per Square | per Square | | Pressure | at Constant | of Outflow | Inch of | Inch of | | per Square | Density | Expanded | Orifice | Orifice if | | Inch | Feet per | Feet per | per Minute | Horse Power | | Pounds | Second | Second | Pounds | = 30 Pounds | | | | | | per Hour | |__________|___________|__________|__________|___________| | | | | | | | 25.37 | 863 | 1401 | 22.81 | 45.6 | | 30. | 867 | 1408 | 26.84 | 53.7 | | 40. | 874 | 1419 | 35.18 | 70.4 | | 50. | 880 | 1429 | 44.06 | 88.1 | | 60. | 885 | 1437 | 52.59 | 105.2 | | 70. | 889 | 1444 | 61.07 | 122.1 | | 75. | 891 | 1447 | 65.30 | 130.6 | | 90. | 895 | 1454 | 77.94 | 155.9 | | 100. | 898 | 1459 | 86.34 | 172.7 | | 115. | 902 | 1466 | 98.76 | 197.5 | | 135. | 906 | 1472 | 115.61 | 231.2 | | 155. | 910 | 1478 | 132.21 | 264.4 | | 165. | 912 | 1481 | 140.46 | 280.9 | | 215. | 919 | 1493 | 181.58 | 363.2 | |__________|___________|__________|__________|____________|

Elbows, globe valves and a square-ended entrance to pipes all offer resistance to the passage of steam. It is customary to measure the resistance offered by such construction in terms of the diameter of the pipe. Many formulae have been advanced for computing the length of pipe in diameters equivalent to such fittings or valves which offer resistance. These formulae, however vary widely and for ordinary purposes it will be sufficiently accurate to allow for resistance at the entrance of a pipe a length equal to 60 times the diameter; for a right angle elbow, a length equal to 40 diameters, and for a globe valve a length equal to 60 diameters.

The flow of steam of a higher toward a lower pressure increases as the difference in pressure increases to a point where the external pressure becomes 58 per cent of the absolute initial pressure. Below this point the flow is neither increased nor decreased by a reduction of the external pressure, even to the extent of a perfect vacuum. The lowest pressure for which this statement holds when steam is discharged into the atmosphere is 25.37 pounds. For any pressure below this figure, the atmospheric pressure, 14.7 pounds, is greater than 58 per cent of the initial pressure. Table 68, by D. K. Clark, gives the velocity of outflow at constant density, the actual velocity of outflow expanded (the atmospheric pressure being taken as 14.7 pounds absolute, and the ratio of expansion in the nozzle being 1.624), and the corresponding discharge per square inch of orifice per minute.

Napier deduced an approximate formula for the outflow of steam into the atmosphere which checks closely with the figures just given. This formula is:

pa W = ---- (49) 70

Where W = the pounds of steam flowing per second, p = the absolute pressure in pounds per square inch, and a = the area of the orifice in square inches.

In some experiments made by Professor C. H. Peabody, in the flow of steam through pipes from ¼ inch to 1½ inches long and ¼ inch in diameter, with rounded entrances, the greatest difference from Napier's formula was 3.2 per cent excess of the experimental over the calculated results.