Chapter 3

4. Let us suppose that the instrument passes from the position I to position III (Fig. 4). Then the ruler C A will come to occupy the position B A, from the fact that the instrument, continuing to move in the same direction, will roll around the point B. It is well, then, to manage so that the system shall have another point of support. For that reason I prolong C B, take B C' = B C, draw C' I, and describe the circumference--the geometrical place of the points C'. I take C' D = C' B and obtain at D the position of the fixed point at which the needle is inserted. In Fig. 4 are represented different positions of the instrument; and it may be seen that all the points C C', and the centers O O', are found upon the circumferences that have their center at I.

5. The manipulation and use of the instrument are of the simplest character. Being given any two straight converging lines whatever, [alpha] [beta] and [gamma] [delta] (Fig. 5), in order to trace all the others I insert a needle at A and arrange the instrument as seen at S. I draw A B and A B', and from there carry it to S' in such a way that the ruler being on [gamma] [delta], one of the resting rulers passes through A. I draw the line C B which meets A B at the point B, the position sought for the second needle. In order to draw the straight lines which are under [alpha] [beta], it is only necessary to hold the needle A in place and to fix one at B', making A B' = A B. In this case S" indicates one of the positions of the instrument.

6. The point A was chosen arbitrarily, but it is evident that that of the needles depends on its distance from the point of convergence. Thus, on taking A' instead of A in the case of Fig. 3, they approach, while the contrary happens on choosing the point A". It is clear that the different positions that a needle A may take are found on a straight line which runs to the point of meeting.

7. If the instrument were jointed or hinged at C, that is to say, so that we could at will modify the angle of the resting ruler, we might make the position of the needles depend on such angle, and conversely.

8. Being given the length C I (Fig. 6), to establish the position of the needles so that all the lines outside of the sheet shall converge at I. To do this, it is well to determine C D, and then to draw the straight line A D B perpendicular to C I, so as to have at A and B the points at which the needles must be placed.

Then

___ ___ ___ AD² CD² CD x DI = AD². CD = ---- = --------- tang²[alpha], DI CI - CD

[TEX: CD \times DI = \overline{AD^2}.\ CD = \frac{\overline{AD^2}}{DI} = \frac{\overline{CD^2}}{CI-CD} \tan^2 \alpha]

whence

CI CD = ------------------ or CD = CI cos²[alpha]. (1) I + tang²[alpha]

[TEX: CD = \frac{CI}{I + \tan^2 \alpha}\ \text{or}\ CD = CI \cos^2 \alpha.]

9. If the instrument is jointed, the absolute values being

_____________ / AD = \ / CD(CI - CD) , (2) \/

[TEX: AD = \sqrt{CD(CI - CD)}]

it suffices to take for CD a suitable value and to calculate AD.

If, for example, the value of C D is represented by C D', the instrument takes the position A' C B', and the needles will be inserted at A' and B' on the line A' D' B', which is perpendicular to C I.

10. If the position of the instrument, and consequently that of the needles, has been established, and we wish to know the distance C I, we will have

CD CI = ------------ ; (3) cos²[alpha]

[TEX: CI = \frac{CD}{\cos^2 \alpha}]

or, again,

___ AC² CI = ----- (4) CD'

[TEX: CI = \frac{\overline{AC^2}}{CD'}]

11. In order to avoid all calculation, we may proceed thus: If I wish to arrange the instrument so that C I represents a given quantity (§ 8), I take (Fig. 7) the length Ci = CI/n, where n is any entire number whatever.

In other terms, Ci is the reduction to the scale of CI.

I describe the circumference C b i a, and arrange the instrument as seen in the figure, and measure the length C b.

It is visible that

C i 1 C b C d ----- = --- = ----- = ------; then C B = n.C b (5) C I n C B C D

CD = n.C d; (6)

and, consequently, the position of the needles which are found at A and B are determined.

12. The question treated in § 10, then, is simply solved. In fact, on describing the circumference C b i a with any radius whatever, I shall have

C B n = -----; (7) c b

and, consequently,

C I = n.C i (8)

13. As may be seen, the instrument composed of three firmly united rulers is the simplest of all and easy to use. Any one can construct it for himself with a piece of cardboard, and give the angle 2 [alpha] the value that he thinks most suitable for each application. The greater 2 [alpha] is, the shorter is the distance at which we should put the needles for a given point of meeting.

14 The jointed instrument may be constructed as shown in Figs 8, 9, and 10. The three pieces, A. B, and C, united by a pivot, O, in which there is a small hole, are of brass or other metal. Rulers may be easily procured of any length whatever. The instrument is Y-shaped. In the particular case in which [alpha] = 180° it becomes T-shaped, and serves to draw parallel lines.

15. The instrument may be used likewise, as we have seen, to draw arcs of circles of the diameter C I or of the radius A O = r, whose center o falls outside the paper. The pencil will be rested on C. We may operate as follows (Fig. 2): Being given the direction of the radii A O and B O, or, what amounts to the same thing, the tangents to the curve at the given points, A and B to be united, we draw the line A D and raise at its center the perpendicular D C, which, prolonged, passes necessarily through the center. It is necessary to calculate the length C D.

We shall have

___ ___ ___ CD (2r - CD) = AD².CD² - 2r.CD + AD² = o.

[TEX: CD (2r - CD) = \overline{AD^2}.\overline{CD^2} - 2r.CD + \overline{AD^2} = o.]

_________ / ___ CD = r ± \ / r² - AD² . \/

[TEX: CD = r ± \sqrt{r^2 - \overline{AD^2}}.]

It is evident that the lower sign alone suits our case, for d < r; consequently,

_________ / ___ CD = r - \ / r² - AD² . (9) \/

[TEX: CD = r - \sqrt{r^2 - \overline{AD^2}}.]

Having obtained C, we put the instrument in the direction A B C. Then each point of C F describes a circumference of the same center o.

16. If the distance of the points A and B were too great, then it would be easy to determine a series of points belonging to the arc of circumference sought (Fig. 4).

Being given C, the direction C I, and C I = R, on C I I lay off C E = d, draw A E B perpendicularly, and calculate C A or A E. I shall have

___ d = (R - d) = AE²;

[TEX: d = (R - d) = \overline{AE^2};]

or, as absolute value,

__________ / A E = \ / d (R - d) . (10) \/

[TEX: AE = \sqrt{d (R-d)}]

The instrument being arranged according to A C B, I prolong C B and take B C' = B C, when C' will be one of the points sought. It will be readily understood how, by repeating the above operations, but by varying the value of d, we obtain the other intermediate points, and how we may continue the operation to the right of C' with the process pointed out.

17. If the three rulers were three arcs of a large circle of a sphere, the instrument might serve for drawing the meridians on such sphere.

18. If we imagine, instead of three axes placed in one plane and converging at one point, a system of four axes also converging in one point, but situated in any manner whatever in space, and if we rest three of them against three fixed points, we shall be able to solve in space problems analogous to those that have just been solved in a plane. If we had, for example, to draw a spherical vault whose center was inaccessible, we might adopt the same method.--_Le Génie Civil_.

* * * * *

FEED-WATER HEATER AND PURIFIER.

[Footnote: A paper read before the Franklin Institute.]

By GEORGE S. STRONG.

In order to properly understand the requirements of an effective feed-water purifier, it will be necessary to understand something of the character of the impurities of natural waters used for feeding boilers, and of the manner in which they become troublesome in causing incrustation or scale, as it is commonly called, in steam boilers. All natural waters are known to contain more or less mineral matter, partly held in solution and partly in mechanical suspension. These mineral impurities are derived by contact of the water with the earth's surface, and by percolation through its soil and rocks. The substances taken up in solution by this process consist chiefly of the carbonates and sulphates of lime and magnesia, and the chloride of sodium. The materials carried in mechanical suspension are clay, sand, and vegetable matter. There are many other saline ingredients in various natural waters, but they exist in such minute quantities, and are generally so very soluble, that their presence may safely be ignored in treating of the utility of boiler waters.

Of the above named salts, the carbonates of lime and magnesia are soluble only when the water contains free carbonic acid.

Our American rivers contain from 2 to 6 grains of saline matter to the gallon in solution, and a varying quantity--generally exceeding 10 grains to the gallon--in mechanical suspension. The waters of wells and springs hold a smaller quantity in suspension, but generally carry a larger percentage of dissolved salts in solution, varying from 10 to 650 grains to the gallon.

When waters containing the carbonates of lime and magnesia in solution are boiled, the carbonic acid is driven off, and the salts, deprived of their solvent, are rapidly precipitated in fine crystalline particles, which adhere tenaciously to whatever surface they fall upon. With respect to the sulphate of lime, the case is different. It is at best only sparingly soluble in water, one part (by weight) of the salt requiring nearly 500 parts of water to dissolve it. As the water evaporates in the boiler, however, a point is soon reached where supersaturation occurs, as the water freshly fed into it constantly brings fresh accessions of the salt; and when this point is reached, the sulphate of lime is precipitated in the same form and with the same tenaciously adherent quality as the carbonates. There is, however, a peculiar property possessed by this salt which facilitates its precipitation, namely, that its solubility in water diminishes as the temperature rises. This fact is of special interest, since, if properly taken advantage of, it is possible to effect its almost complete removal from the feed-water of boilers,

There is little difference in the solubility of the sulphate of lime until the temperature has risen somewhat above 212° Fahr., when it rapidly diminishes, and finally, at nearly 300°, all of this salt, held in solution at lower temperatures, will be precipitated when the temperature has risen to that point. The following table[1] represents the solubility of sulphate of lime in sea water at different temperatures:

Temperature. Percentage Sulph. Fahr. Lime held in Solution. 217° 0.500 219° 0.477 221° 0.432 227° 0.395 232° 0.355 236° 0.310 240° 0.267 245° 0.226 250° 0.183 255° 0.140 261° 0.097 266° 0.060 271° 0.023 290° 0.000

[Footnote 1: _Vide_ Burgh, "Modern Marine Engineering," page 176 _et seq._ M. Cousté, _Annales des Mines_ V 69. _Recherches sur Vincrustation des Chaudières a vapour_. Mr. Hugh Lee Pattison, of Newcastle-on-Tyne, at the meeting of the Institute of Mechanical Engineers of Great Britain, in August, 1880, remarked on this subject that "The solubility of sulphate of lime in water diminishes as the temperature rises. At ordinary temperatures pure water dissolves about 150 grains of sulphate of lime per gallon; but at a temperature of 250° Fahr., at which the pressure of steam is equal to about 2 atmospheres, only about 40 grains per gallon are held in solution. At a pressure of 3 atmospheres, and temperature of 302° Fahr., it is practically insoluble. The point of maximum solubility is about 95° Fahr. The presence of magnesium chloride, or of calcium chloride, in water, diminishes its power of dissolving sulphate of lime, while the presence of sodium chloride increases that power. As an instance of the latter fact, we find a boiler works much cleaner which is fed alternately with fresh water and with brackish water pumped from the Tyne when the tide is high than one which is fed with fresh water constantly."]

These figures hold substantially for fresh as well as for sea water, for the sulphate of lime becomes wholly insoluble in sea water, or in soft water, at temperatures comprised between 280° and 300° Fahr.

It appears from this that it is simply necessary to heat water up to a temperature of 250° in order to effect the precipitation of four fifths of the sulphate of lime it may have contained, or to the temperature of 290° in order to precipitate it entirely. The bearing of these facts on the purification of feed-waters will appear further on. The explanation offered to account for the gradually increasing insolubility of sulphate of lime on heating, is, that the hydrate, in which condition it exists in solution, is partially decomposed, anhydrous calcic sulphate being formed, the dehydration becoming more and more complete as the temperature rises. Sulphate of magnesia, chloride of sodium (common salt), and all the other more soluble salts contained in natural waters are likewise precipitated by the process of supersaturation, but owing to their extreme solubility their precipitation will never be effected in boilers; all mechanically suspended matter tends naturally to subside.

Where water containing such mineral and suspended matter is fed to a steam boiler, there results a combined deposit, of which the carbonate of lime usually forms the greater part, and which remains more or less firmly adherent to the inner surfaces of the boiler, undisturbed by the force of the boiling currents. Gradually accumulating, it becomes harder and thicker, and, if permitted to accumulate, may at length attain such thickness as to prevent the proper heating of the water by any fire that may be maintained in the furnace. Dr. Joseph G. Rogers, who has made boiler waters and incrustations a subject of careful study, declares that the high heats necessary to heat water through thick scale will sometimes actually convert the scale into a species of glass, by combining the sand, mechanically separated, with the alkaline salts. The same authority has carefully estimated the non-conducting properties of such boiler incrustations. On this point he remarks that the evil effects of the scale are due to the fact that it is relatively a nonconductor of heat. As compared with iron, its conducting power is as 1 to 37½, consequently more fuel is required to heat water in an incrusted boiler than in the same boiler if clean. Rogers estimates that a scale 1-16th of an inch thick will require the extra expenditure of 15 per cent. more fuel, and this ratio increases as the scale grows thicker. Thus, when it is one-quarter of an inch thick, 60 per cent. more fuel is needed; one-half inch, 112 per cent. more fuel, and so on.

Rogers very forcibly shows the evil consequences to the boiler from the excessive heating required to raise steam in a badly incrusted boiler, by the following illustration: To raise steam to a pressure of 90 pounds the water must be heated to about 320° Fahr. In a clean boiler of one-quarter inch iron this may be done by heating the external surface of the shell to about 325° Fahr. If, now, one-half an inch of scale intervenes between the boiler shell and the water, such is its quality of resisting the passage of heat that it will be necessary to heat the fire surface to about 700°, almost to a low red heat, to effect the same result. Now, the higher the temperature at which iron is kept the more rapidly it oxidizes, and at any heat above 600° it very soon becomes granular and brittle, and is liable to bulge, crack, or otherwise give way to the internal pressure. This condition predisposes the boiler to explosion and makes expensive repairs necessary. The presence of such scale, also, renders more difficult the raising, maintaining, and lowering of steam.

The nature of incrustation and the evils resulting therefrom having been stated, it now remains to consider the methods that have been devised to overcome them. These methods naturally resolve themselves into two kinds, chemical and mechanical. The chemical method has two modifications; in one the design is to purify the water in large tanks or reservoirs, by the addition of certain substances which shall precipitate all the scale-forming ingredients before the water is fed into the boiler; in the other the chemical agent is fed into the boiler from time to time, and the object is to effect the precipitation of the saline matter in such a manner that it will not form solid masses of adherent scale. Where chemical methods of purification are resorted to, the latter plan is generally followed as being the least troublesome. Of the many substances used for this purpose, however, some are measurably successful; the majority of them are unsatisfactory or objectionable.

The mechanical methods are also very various. Picking, scraping, cleaning, etc., are very generally resorted to, but the scale is so tenacious that this only partially succeeds, and, as it necessitates stoppage of work, it is wasteful. In addition to this plan, a great variety of mechanical contrivances for heating and purifying the feed-water, by separating and intercepting the saline matter on its passage through the apparatus, have been devised. Many of these are of great utility and have come into very general use. In the Western States especially, where the water in most localities is heavily charged with lime, these mechanical purifiers have become quite indispensable wherever steam users are alive to the necessity of generating steam with economy.

Most of these appliances, however, only partly fulfill their intended purposes. They consist essentially of a chamber through which the feed-water is passed, and in which it is heated almost to the boiling point by exhaust steam from the engine. According to the temperature to which the water is heated in this chamber, and the length of time required for its passage through the chamber, the carbonates are more or less completely precipitated, as likewise the matter held in mechanical suspension. The precipitated matter subsides on shelves or elsewhere in the chamber, from which it is removed from time to time. The sulphate of lime, however, and the other soluble salts, and in some cases also a portion of the carbonates that were not precipitated during the brief time of passage through the heater, are passed on into the boiler.

Appreciating this insufficiency of existing feed-water purifiers to effectually remove these dangerous saline impurities, the writer in designing the feed-water heater now to be described paid special attention to the separation of all matters, soluble and insoluble; and he has succeeded in passing the water to the boilers quite free from any substance which would cause scaling or coherent deposit. His attention was called more particularly to the necessity of extreme care in this respect, through the great annoyance suffered by steam users in the Central and Western States, where the water is heavily charged with lime. Very simple and even primitive boilers are here used; the most necessary consideration being handiness in cleaning, and not the highest evaporative efficiency. These boilers are therefore very wasteful, only evaporating, when covered with lime scale, from two to three pounds of water with one pound of the best coal, and requiring cleansing once a week at the very least. The writer's interest being aroused, he determined, if possible, to remedy these inconveniences, and accordingly he made a careful study of the subject, and examined all the heaters then in the market. He found them all, without exception, insufficient to free the feed-water from the most dangerous of impurities, namely, the sulphate and the carbonate of lime.

Taking the foregoing facts, well known to chemists and engineers, as the basis of his operations, the writer perceived that all substances likely to give trouble by deposition would be precipitated at a temperature of about 250° F.

His plan was, therefore, to make a feed-water heater in which the water could be raised to that temperature before entering the boiler. Now, by using the heat from the exhaust steam the water may be raised to between 208° and 212° F. It has yet to be raised to 250° F.; and for this purpose the writer saw at once the advantage that would be attained by using a coil of live steam from the boiler. This device does not cause any loss of steam, except the small loss due to radiation, since the water in any case would have to be heated up to the temperature of the steam on entering the boiler. By adopting this method, the chemical precipitation, which would otherwise occur in the boiler, takes place in the heater; and it is only necessary now to provide a filter, which shall prevent anything passing that can possibly cause scale.

Having explained as briefly as possible the principles on which the system is founded, the writer will now describe the details of the heater itself.