98 THE VICTORIAN INSTITUTE OF ENGINEERS.

PAPER

TRANSMISSION OF COMPRESSED AIR IN PIPE SYSTEMS.

By Johan Sarvaas.

The transmission of power by compressed air is accom-panied by a high percentage of loss. Nevertheless this me-dium of transmission in certain mining and civil engineering operations is used in preference to its more economic rival, electricity, on account of its inherent properties as a gas, and the fact that certain types of machines, notably rock-drilling machinery, designed to be driven by compressed air, are far superior to any types of electrically-driven rock drill yet devised.

A considerable amount of the loss experienced in the transmission of power by compressed air is that lost in the pipes between the air received and the machines. We must therefore endeavour to give careful consideration to so design the pipe systems that the losses may be reduced to a mini-mum.

This paper will be confined therefore to the estimation of the flow and loss of pressure in pipe systems for compressed air transmission.

The frictional losses in the case of both water and air vary directly as the perimeter and length of the pipe, directly as the square of the velocity of flow and inversely as the area, or in symbols: If P be the perimeter in feet, L the length in feet, . V the velocity in feet per second, A the area in square feet, then h; the head lost in overcoming friction, is

h = tPLV 2 (I.) A

where f is some constant.

The quantity P is called the hydraulic radius, and can be

denoted in the case of circular pipes by 4D where D is the diameter of the pipe.

We may therefore write the above formula in the follow-ing form

V = c V Dh/L (II.) This is know as the D'Arcy formula, and up to this point the theory is applicable to either liquids or gases, that is to say to both inelastic and elastic fluids. We are chiefly indebted

to D'Arcy for its practical application to elastic fluids such as compressed air.

For elastic fluids the formula takes the form V = c ✓ D (P1 – P,)/W 1L (III.)

Where P, is the initial gauge pressure in lbs. per sq. in. Where P2 is the final gauge pressure in lbs. per sq. in. Where W1 the density or weight in lbs. per cubic foot at the

initial pressure P1. It will be recognised that P1 – P2 gives equivalent motive

W1 pressure expressed in feet.

Next let Q = discharge in cubic feet per second. Q = VA = 7r D2 . c D (P1 – P,)/W1 L (IV.) 4

1I

Hence Q = c V D5 I P, – P,

V 1 W, D'Arcy conducted experimental researches for the determin-ation of c for different diameters of pipe expressed in inches, and values of Q in cubic feet per minute. Values are given in Table I. for the coefficient for pipes ranging in diameter from 1 inch to 16 inches, and for still greater convenience in making numerical computations corresponding values have been computed for c ✓ D5.

Taking the weight of a cubic foot of air at average atmos-pheric pressure and temperature as .0761 lbs, the densities for other gauge pressures may be obtained with sufficient accuracy for practical purposes as follows:—

W1 = 0761 (Pi + 14..1 – .0761 (.o68P1 + I) l 14.7 / P1 being the gauge pressure for which we require the value of W,.

Values for W1 and ✓ W1 are given in Table II.

When, as is generally the case, we desire to know the equivalent volume of free air corresponding to the volume of compressed air at the terminal pressure P2, as related to the density of the atmosphere, the following formula may be used:-

F=q x W2 Where F is the equivalent free air in feet per minute.

W, _ .o68P, + 1, from which Table III. has been compiled. = discharge of compressed air in cubic feet per minute

at the terminal pressure P, lbs. per square inch (gauge).

(V.)

(

COMPRESSED AIR IN PIPE SYSTEMS. 99

100 THE VICTORIAN INSTITUTE OF ENGINEERS.

With the aid of these three tables we can now proceed with practical computations; but to still further facilitate these Table IV. has been compiled for pressures ranging from 6o to boo lbs. per square inch, and for pressure losses from I to

io lbs., giving values of ✓ P, P2

Wl

Example (3).

A 280 cftper min, bip free air

C 350 c ft permin goo' .5 900' free air

D 400 ell per rnin free air

F300 c/icermia free air

To illustrate the practical application of the tables, sup-pose an engineer is called upon to supply the above quanti-ties of free air compressed to 8o lbs. per square inch at A, C, D, and F, and that H is the receiver at the generating station where the pressure is maintained at ioo lbs. per square inch, the length of all pipes being given and positions of branches from Table III.

6.44 = 43.4 cubic ft. per minute at 8o lbs. per square in. at A

350 = 54.3 cubic ft. per minute at 8o lbs. per square in. at C

6.44

300 = 46.5 cubic ft. per minute at 8o lbs. per square in. at F 6.44

Now if we decide to limit the drop of pressure from B to A and B to C to 5 lbs., also from E to D and E to F to 5 lbs., and again the drop from G to B or G to E to 5 lbs., we will have an available drop of io lbs. from H to G. The pres-sures at H, G, B, and E may therefore be fixed at roo, go, "85 and 85 lbs. per square inch respectively, provided we allow suitable diameters for the various pipes.

To deliver 43.4 cubic feet per minute from B at 85 lbs. to A at 8o lbs. per square inch, the distance being i600 feet, we apply formula (V.).

4900

625'

2 8o

6.44. 400 — 62.1 cubic ft. per minute at 8o lbs. per square in. at D

COMPRESSED AIR IN PIPE SYSTEMS. IO•i

Using the tables:—Pl – P2 Table IV. = 3.115 w1

C V D5 43.4 = 40

this gives C V D5 = 557

And from Table I. we conclude that a pipe between 2 and 3 in. diameter is required, say 2-i in. diameter. A similar calculation for the pipe BC would suggest a pipe of 22 in. also.

Dealing with pipes ED and EF in the same, way, we get diameters of 2i in. and 24 in. respectively. There must

therefore exist at B a volume of air = 97'85 x 80 = 91.8

cubic feet per minute at 85 lbs. per square inch pressure, and in the same way a volume equal to 102.2 cubic feet per minute at 85 lbs.. per square inch at E

5

91.8 – C 30 x 3.017 t- ✓ D5 =906

which from Table I. suggests a pipe a little more than 3 in. diameter, say 3i in.

Similarly for pipe GE a pipe somewhere about 4 in. dia-meter should suffice.

We would require at G a flow of air equal to (91.8 + IO2.2) x 85 = 184.3 cubic feet per minute at

90 90 lbs. per square inch pressure.

Finally we have for the main trunk supply HG 5 184.3 = C ✓ D x 4.101.

Hence C ✓ D diameter for HG.

314.5, which suggests a pipe 5 in,

The air supply from the receiver at H would be 184.3 x go – 165.87 cubic feet per minute at ioo lbs. per

mo square inch, which would necessitate the compression by the air compressor and the delivery into the receiver H of 165.87 x 7.8o = 1294 cubic feet of free air per minute,

h e o o

t r

r

1

x 3.115

70

102 THE VICTORIAN INSTITUTE OF ENGINEERS.

TABLE I.

Diameter. Coefficient-.

in. C CV D5

1 .. 45.3

2 52.7

3 56.1

4 57.8

5 58.4

6 59.5

7 60.1

8 60.7

9 61.2

10 .. 61.8

12 62.1

14 .. 62.3

16 62.6

45.3 297 876

1,856 3,298 5,273 7,817

10,988 14,872 19,480 30,926 45,690 64,102

TABLE II.

Gauge Pressure.

lb. sq. in. W1 `/ W1

0 .. .0761 .276

5 .1020 .319

10 .. 1278 .. .358

15 . .1537 .392

20 .1796 _ .424

25 .2055 .463

30 .2313 .481

35 .2572 .507

40 .2831 .532

45 .3090 .556

50 .. .3348 .. .578

55 .3607 .600

60 .. .3866 .622

65 .4125 .642

70 .4383 .662

75 .4642 .. .681

80 .4901 .700

85 .. .5160 .718

90 .. .5418 .736

95 .5677 .. .753

100 .. .5936 .770

COMPRESSED AIR IN PIPE SYSTEMS. I03

TABLE III.

P2

lb. sq. in. P2

lb. sq. in. w3

0 1.00 55 .. 4.74 5 1.34 60 5.08

10 .. 1.68 65 5.42 15 ... 2.02 70 5.76 20 2.36 75 6.10 25 2.70 80 6.44 30 3.04 85 .. 6.78 35 3.38 90 7.12 40 3.72 95 .. 7.46 45 4.06 100 .. 7.80 50 4.40

104 THE VICTORIAN INSTITUTE OF ENGINEERS.

TABLE IV.

Values of %/. w, - in D'Arcy's Formula.

N

oS cc:

Loss of Pressure equals Pl P2.

2)

â A u 11b. 21b. 31b. 41b. 51b. 61b. 71b. 81b. 91b. 101b.

P2 P2

lb. lb.

60 1.597 2.242 2.730 3.132 3.479 3.787 4.066 4.320 4.557 4.775 60 61 1.586 2.228 2.712 3.112 3.458 3.764 4.042 4.294 4.530 4.747 61 62 1.576 2.214 2.695 3.092 3.437 3.742 4.019 4.268 4.503 4.718 62 63 1.566 2,200 2.678 3.074 3.417 3.720 3.995 4.244 4.476 4.693 63 64 1.556 2.186 2.662 3.056 3.397 3.698 3.971 4.220 4.452 4.668 64 65 1.546 2.173 2.647 3.038 . 3.376 3.676 3.948 4.196 4.428 4.642 65 66 1.537 2.160 2.631 3.020 3.356 3.654 3.926 4.172 4.404 4.617 66 67 1.528 2.147 2.615 3.002 3.337 3.634 3.905 4.150 4.380 4.592 67 68 1.519 2.134 2.600 2.984 3.318 3.615 3.884 4.128 4.356 4.566 68 69 1.511 2.122 2.584 2.968 3.300 3.596 3.863 4.104 4.332 4.541 69 70 1.501 2.106 2.570 2.952 3.283 3.576 3.842 4.082 4.308 4.516 70 71 1.492 2.098 2.556 2.936 3.265 3.556 3.820 4.060 4.284 4.494 71 72 1.484 2.086 2.543 2.920 3.247 3.537 3.799 4.038 4.263 4.471 72 73 1.476 2.075 2.529 2.904 3.229 3.517 3.778 4.018 4.242 4.449 73 74 1.468 2.064 2.515 2.888 3.211 3.498 3.759 3.998 4.221 4.427 74 75 1.460 2.052 2.501 2.872 3.193 3.480 3.741 3.978 4.200 4.405 75 76 1.452 2.041 2.487 2.856 3.177 3.463 3.723 3.958 4.179 4.383 76 77 1.444 2.030 2.473 2.842 3.162 3.446 3.704. 3.938 4.158 4.361 77 78 1.436 2.019 2.461 2.828 3.146 3.429 3.686 3.918 4.137 4.339 78 79 1.428 2.009 2.449 2.814 3.130 3.412 3.667 3.898 4.116 4.317 79 80 1.421 1.999 2.437 2.800 3.115 3.395 3.648 3.878 4.095 4.294 80 81 1.414 1.989 2.425 2.786 3.090 3.377 3.630 3.858 4.074 4.272 81 82 1.407 1.979 2.413 2.773 3.084 3.360 3.611 3.840 4.053 4.253 82 83 1.400 1.969 2.401 2.758 3.068 3.343 3.593 3.820 4.035 4.234 83 84 1.393 1.959 2.388 2.744 3.052 3.326 3.575 3.802 4.017 4.215 84 85 1.386 1.949 2.376 2.730 3.037 3.310 3.559 3.786 3.999 4.196 85 86 1.379 1.939 2.364 2.716 3.022 3.294 3.543 3.768 3.981 4.177 86 87 1.372 1.929 2.352 2.702 3.008 3.279 3.527 3.752 3.963 4.158 87 88 1.365 1.920 2.340 2.690 2.994 3.265 3.511 3.734 3.945 4.139 88 89 1.358 1.910 2.338 2.678 2.981 3.250 3.495 3.718 3.927 4.120 89 90 1.351 1.901 2:319 2.666 2.967 3.235 3.479 3.700 3.909 4.101 90 91 1.345 1.893 2.309 2.654 2.954 3.221 3.463 3.684 3.891 4.082 91 92 1.339 1.884 2.298 2.642 2.940 3.206 3.447 3.666 3.873 4.064 92 93 1.333 1.876 2.288 2.630 2.927 3.191 3.432 3.650 3.855 4.048 93 94 1.327 1.867 2.278 2.618 2.914 3.177 3.416 3.634 3.840 4.032 94 95 1.321 1.859 2.267 2.606 2.900 3.162 3.401 3.618 3.825 4.016 95 96 1.315 1.850 2.257 2.594 2.887 3.148 3.387 3.604 3.810 4.000 96 97 1.309 1.842 2.246 2.582 2.873 3.135 3.373 3.590 3.795 3:984 97 98 1.303 1:833 2.236 2.570 2.862 3.123 3.360 3.576 3.780 3.969 98 99 1.297 1.825 2.226 2.560 2.851 3.110 3.347 3.562 3.765 3.953 99

100 1.291 1.817 2.217 2.550 2.840 3.098 3.334 3.548 3.750 3.937 100

CURRENT EXCHANGES.

DISCUSSION Mr. J. T. N. ANDERSON moved a vote of thanks to 't Ÿîe lec-

turer for having brought forward a subject of great import-ance, and which was not contained in the recognised text books. He presumed that the calculations were made as-suming isothermal* conditions throughout.

Mr. SARVAAS said that was so. Mr. J. N. REESON , seconded the vote of thanks. He had

listened with much interest to the paper, inasmuch as the problems dealt with were often experienced in the ordinary practice of the engineer. Somewhat similar problems were met with in his own experience, but they dealt with much löwer pressures and more complex pipe systems; whilst the material they were using was much lighter than air. The formula they usually followed was Unwin's, which, he thought, was the latest applicable to gas. The tables Mr. Sarvaas had taken such trouble in compiling would prove of great value to engineers and mine managers who had to compute the sizes of pipes capable of carrying air at the pressures re-quired.

The vote of thanks was carried with acclamation.

DIGEST OF ARTICLES ON CURRENT EXCHANGES.

Mr. WM. CHAS. ROWE said he was sorry no one had taken advantage of the digest of exchanges given at the last meet-ing. The matter was purely an experiment; it entailed a good deal of work, and would only be continued if it proved to be serving a useful purpose in the Institute.

The Proceedings of the North-East Coast of the Insti-tution of Engineers and Shipbuilders contained an article on "Pulverised Fuel in Some Commercial Aspects." A number of articles on pulverised fuel had appeared recently, but they were largely advertisements of some particular commodity. An interesting article was that on "A New Form of Bow Con-struction"-a soft-ended ship to prevent initial injury in col-lision. "A New Electrical Drive for Ships and Other Auxil-iaries" was well worth reading. "Further Development of . Large Power Diesel Engines", The Longitudinal Strength of Ships"; "Internal Combustion Locomotives"; "An Investigation into the Effect of Cold Drawing upon Some Properties of Steel and Iron"; "Steam Pipes for Extra High Pressure"—a very interesting paper, which also described bends made of corrugated pipe, giving the maximum of flexibility; "The Manufacture of Pressed Condenser Tubes"; "The Internal Combustion Turbine"; "Canadian Bulk Cargo Vessels on the Great Lakes."

I05

106 THE VICTORIAN INSTITUTE OF ENGINEERS.

From the Annual Volume of the Smithsonian Institute, 1924, much interest would be found in an article, "The Vacuum, There's Something in It," and also "Clear Fused Quartz Made in the Electric Furnace."

From the American Society of Mechanical Engineers, vol. 46 (i924) came the following:—"Vibration in Steam Turbine Disc Wheels"—a very valuable paper; "Temperature and Stress Distribution in Hollow Cylinders" (mathematical); "Gas Lngines in the Steel Industry"; "The Emmet Mercury Vapour Process"—power produced from mercury vapour instead of steam; "The Effect of Temperature Upon the Properties of Metals"--this paper had a very fine bibliography; "Re-super-heating in Turbines"; "Recent Applications of Powdered Coal to Boilers"; "Production Control"; "The Temperatures of Evaporation of Water into Air"; "A Graphic Study of Journal Lubrication"; "Strength of Gear Teeth"; "Mechanical Springs: Strength and Proportions of Wheel Centres"; "Experimental investigation of Nozzle Efficiency"; "Steam Turbine"; "Large Oil Engines"; "Gas Turbines"; "Intakes for Power Plants"— experiments with large scale models; "Design of Penstocks"; "Zoelly Turbine-driven Locomotive"—describing 1000-2000 h.p. turbo-locomotives, an article particularly interesting to railway men.

Mr. J. N. REESON said the thanks of the Institute were due to Mr. Rowe for extracting such valuable suggestions from the exchanges. It would be a great advantage if means could be found of circulating the extracts to members, and if the extracts could be included with the notice paper it would probably help to stimulate interest in the matter.

Mr. J. T. N. ANDERSON supported the previous remarks Most of the large societies issued similar extracts to their members, the Institution of Civil Engineers making an annual charge of io/- for the service. It would be of great advan-tage to members if Mr. Rowe's extracts could be supplied to them. By undertaking that work Mr. Rowe had added to the heavy debt the Institute owed him for having taken charge of the library.

Mr. ROWE said the extracts were published in the last Proceedings, and he understood it was the intention to con-tinue their publication. It was useless to merely stuff one's shelves with scientific works; the proper method was to have a card index, so that any matter required could be conveni-ently referred to at any time. He frequently thought mem-bers did not receive adequate return for the money spent an-nually on periodicals. Would it not be better to pay a cer-tain subscription in order that some competent person should

TRAPPING WEEDS IN WATER MAINS. IOC

select extracts, and record them on a card index which would be available to subscribers at any time. From the commer-cial point of view it would be more economical, and they would receive a better utility.

Mr. A. CASSON SMITH said Mr. Rowe's suggestion was a good one. They did not want to stock their minds with a lot of matter they would never require. The value lay in having it at hand if it were needed, and that could only be done by a card index.

Mr. J. N. REESON said hé appreciated the value of the suggestion. The great difficulty was that one read an article in a scientific magazine or technical journal, but when in practice that particular information was required the article could not be found. The card index would save a mass of information that would otherwise be irretrievably lost

TRAPPING WEEDS IN WATER MAINS. • A Question Raised by a Country Member.

Mr. J. T. N. ANDERSON said a great deal of information would be required before advice could be given on such a matter. He presumed the pipes in question were of iron, and iron pipes were subject to a great number of growths—some vegetable, some almost inorganic. The first thing necessary for the removal of those growths was to ascertain whether they were iron growths, which were generally acid in their re-action; or whether they arose from some othercause, which were generally calcareous or alkaline. In the case of acid it was usual to treat it with lime; whilst sulphate of copper was used for alkaline. Those questions were generally not for botanists or bacteriologists, but rather for industrial chemists in conjunction with the engineer. He would advise that the matter be attacked by rule of thumb methods with the help of a competent chemist. The academic question as to what the weeds were was, of course, very interesting, but from the commercial point of view it was of very little value. A point to be borne in mind was that after getting rid of the weed steps should be taken to prevent its recurrence. Some me-thod should be employed to clear the water of the food which those weeds or ammalculae thrived upon. If the water' en-tered the pipes at a high temperature the growths in the pipes were increased tenfold. He would strongly advise that the experiment of drawing the water from a greater depth be tried.

Library Digitised Collections

Author/s:

Sarvaas, Johan

Title:

Transmission of compressed air in pipe systems

Date:

1927

Persistent Link:

http://hdl.handle.net/11343/24667

File Description:

Transmission of compressed air in pipe systems