PROCEEDINGS
of the Tomsk Technological Institute
of Emperor Nicholas II.

Vol. 18. 1910, No. 2.

VII.

V. N. Pinegin.

REVIEW OF THE WORKS OF A. Ya. MILOVICH.

1–7.

Review of the Works of A. Ya. Milovich.

Mr. Milovich, as an applicant for the chair of hydraulics and hydraulic engines at the Tomsk Technological Institute, has submitted two articles:

“Designing the blades of a Francis turbine by Pfarr’s method.”

“An experiment in the theory of the suction pipe.”

These works, as is evident from the notes made at the beginning of each article, were appended by him to the report on his foreign assignment (1903–1905) and appeared in print at the beginning of 1907.

Working abroad in educational institutions made famous by the names of such scholars as Pfarr and Prasil, Mr. Milovich, of course, must have become imbued with the ideas proceeding from the chairs of these giants of hydraulics. Carried away by these ideas and having assimilated them, he conceived the plan of acquainting Russian engineers with them, since at that time the newest hydrodynamic theory of Prasil’s was little known among us,¹ while of Pfarr, who was chiefly a practical designer-constructor in turbine building, people knew only by hearsay.²

Somewhat later than Prasil, and in a somewhat different form, Prof. Lorentz³ (Danzig) gave a hydrodynamic theory of turbines. The relation of Prasil’s theory to Lorentz’s theory is the relation of the general to the particular; moreover, some propositions of Lorentz’s are not entirely free from errors, as was shown, for example, by Stodola,⁴ and also by Prasil.⁵ These

¹ It first appeared in print in 1903 under the title: Ueber Flüssigkeitsbewegungen in Rotationshohlräumen. Schweiz. Bauz. 1903, Nos. 18, 21, 22, 25, and 27; and, as a continuation of these investigations: Die Bestimmung der Kranzprofile und der Schaufelformen für Turbinen und Kreiselpumpen. Schweiz. Bauz. 1906, Nos. 23, 24, 25.

² His book—Die Turbinen für Wasserkraftbetrieb—appeared at the beginning of 1907.

³ Neue Grundlagen der Turbinentheorie. Zeitschr. für das gesammte Turbinenwesen. 1905, Nos. 17, 18, 19, 20, and later in a separate edition: Neue Theorie u. Berechnung der Kreiselräder. 1909.

⁴ Stodola. Zur Theorie der Dampfturbine. Zeitschr. f. d. ges. Turbinenwesen. 1907. H. 16.

⁵ Die Bestimmung der Kranzprofile und der Schaufelformen für Turbinen u. Kreiselpumpen. Schweiz. Bauz. 1906, No. 25.

Lorentz’s works apparently remained unknown to Mr. Milovich, as did the latest article by Mr. Prasil.

But it was not only a desire to acquaint Russian engineers with a new direction in turbine construction that guided Mr. Milovich. Already in his first work, “Construction of Francis Blades by Pfarr’s Method,” a work that is the least original, Mr. Milovich also sets himself another aim: he intends to clarify the theoretical foundations of blade construction, since, in his opinion, both Prasil and Pfarr present their ideas from their lecterns insufficiently clearly, “probably,” he says, “owing to their relative difficulty”¹. “The latter circumstance,” he says further,² “in connection with the lack felt in Russian literature of indications concerning the question that interests us, has prompted me to come forward with the exposition, offered below, of Prof. Pfarr’s method, the chief purpose of which is an attempt to elucidate its theoretical foundations and practical applications.”

At the same time, however, this very difficulty of the question “does not permit Mr. Milovich to present the theoretical considerations on the questions touched upon here in all their completeness,” but only “to confine himself to general guiding indications.” As regards the first aim—acquainting Russian engineers with Pfarr’s method—at the present time, after the appearance of Pfarr’s own manual (Die Turbinen für Wasserkraftbetrieb), it has lost all significance. The second aim—to give the theoretical foundations of certain propositions of Pfarr—on the one hand, because of the appearance of Pfarr’s book, likewise loses its significance, since Pfarr had the opportunity here to illuminate all his propositions much more fully than in his lectures; and on the other hand, Mr. Milovich does not always achieve this aim with sufficient persuasiveness. Thus, for example, transferring the entire center of gravity of the construction of the blades of a Francis turbine to the outlet profile of the runner, he, in the theoretical consideration of the flow of water through the turbine channels, assumes the blades to be as if nonexistent, does not at all consider the influence of external friction, and diminishes the importance of the centrifugal force acting on the particles of water. Meanwhile, in the presence of these conditions, the form of the flow will of course change; the form of the surface of equal velocity potential, which is obtained without taking into account the above-mentioned conditions of motion, will also change; and Mr. Milovich especially insists on coordinating the construction of the blades with this surface. External friction in the given

chance plays a large role, and it is hardly well founded to insist on the unconditional fulfillment of theoretical requirements derived under the presumed absence of this friction.

And Pfarr himself, pointing to the requirement of theoretical reasoning that the outlet curve be constructed perpendicular to the streamlines, does not advise, in designing, that this rule be strictly followed, indicating that in this case the external friction, proportional to the path, would increase greatly owing to the increase in the length of the blades¹; for high-speed turbines, however, he finds such blades entirely unsuitable, as excessively increasing the path of the water in the wheel and, consequently, the friction as well. Criticizing at the same time the American construction of blades as allowing the water to deviate from the form of flow laid down as the basis of the construction, and the construction built according to purely theoretical considerations, Pfarr advises always keeping to the middle, not deviating very much to one side or the other, although at the same time he himself points out that some American turbines give a very good coefficient of efficiency, notwithstanding sometimes even the excessively extraordinary forms of the blades, as, for example, in turbines of the “Hercules” system².

On p. 6 of his work Mr. Milovich, pointing to the circumstance that “upon entering a curved channel the jets of liquid are inclined to the line of entry,” draws, it seems to me, too hasty a conclusion: that “the angle of the jets of liquid, upon entering a curved channel, is always different from the angle of the walls of the latter with the surface of admission,” and further, that “the indicated circumstance makes obvious the uselessness of an exact determination of the blade angles,” whereas above the discussion concerns only the angle of the streamlines with the vertical line, and not the angle of the channel walls with the whole surface of admission; and then the influence of the guide apparatus is completely ignored.

In the last paragraph, speaking of the stability of the coefficient of efficiency, Mr. Milovich leaves out of account the influence of the method of regulation on the stability of the machine’s operation, which is of great importance: regulation, for example, by slide gates gives much less stability than Zodel’s regulation, and the latter less than Fink’s regulation.

I now turn to Mr. Milovich’s second article: “An Attempt at a Theory of the Suction Pipe.”

First of all, it seems to me, the author at once took the wrong

...point of view regarding his own work, regarding it as having effected, as it were, a revolution in the doctrine of the draft tube.

In his preface he says, for example: “Up to the very latest time, with regard to the guide apparatus and the draft tube, only insignificant remarks were made” (p. 1); “the hydrodynamic theory of flows and the forms they have found, though few in number, make it possible, in my opinion, to lay a complete foundation for the theories both of the guide apparatus and of the turbine chamber, and of its draft tube” (p. 2). “The latter [the theory of the draft tube], as it has been set forth up to now by all authors, is very simple and has as its aim only the determination of the pressure at each point inside the tube” (p. 4), and then, having briefly presented the old theory of the draft tube, based on the application of Bernoulli’s equation, he concludes this exposition with the words: “apart from the scanty remarks of certain authors, which in essence introduce nothing new, the exposition presented contains everything that was known concerning the draft tube up to the present time” (p. 7).

Reading all these lines, one might have thought that the author was completely unfamiliar either with Prasil’s works or with Lorentz’s works (with the latter, as I have already indicated above, he apparently was indeed unfamiliar); because, knowing, for example, Prasil’s works, it is difficult to say that a theory of the draft tube based on the theory of flows did not exist before Mr. Milovich’s work. Indeed, Mr. Milovich’s work itself is nothing other than a reworking of Prasil’s work, supplemented only by certain conclusions.

The author himself goes on to say: “the development of the proposed theory of the draft tube on the basis of the theory of flows was aided by Prof. Prasil’s article—Ueber Flüssigkeitsbewegungen in Rotationshohlräumen, in which one of the possible forms of draft tubes is also indicated” (p. 8), and further, that Prof. Pfarr in 1905 introduced into his course the theory of the draft tube according to Prasil; on p. 30 and the following pages he even gives Prasil’s tube and describes the method of constructing it. In further criticizing the latter tube, Mr. Milovich criticizes not the hydrodynamic theory itself, on the basis of which it was obtained, and the exposition of which he himself uses, but only its form, symmetrical with respect to the axis—a form that follows strictly from the hydrodynamic theory of flows, but one that is, admittedly, unsatisfactory with respect to the exit conditions; Prasil’s merit consists precisely in the fact that he was the first to provide a hydrodynamic theory for constructing both the runner itself and the draft tube. It remained for Mr. Milovich only to supplement and modify, not to create anew.

I now turn to a more detailed analysis of the work. In § 1 the author sets forth, as I have already said above, the theory of the draft tube according to Graf (Theorie, Berechnung und Konstruktion der Wasserturbinen und deren Regulatoren), on the basis of Bernoulli’s theorem; the remarks concerning the permissible height of the draft tube are close to those of Pfarr (see Die Turbinen für Wasserbetrieb, p. 178). § 2 contains a “critical assessment of the existing views on the draft tube,” where by a draft tube the author again understands only a tube constructed on the basis of Bernoulli’s theorem.

§§ 3, 4, and 5 contain an exposition of Prasil’s hydrodynamic theory and of the conclusions at which Prasil arrived concerning streamlines, the magnitude of velocity, surfaces of equal relative and absolute velocities, and surfaces of equal pressure (the latter, although not indicated by Prasil, are obtained from the equation that has been derived for this surface).

In § 6 (pp. 18–21) the author sets forth the laws of plane motion of a fluid and lines of equal pressure. All these questions have long since been studied by Euler, Helmholtz, Kirchhoff, Riemann–Weber, Wien, and others, though, of course, without any indication of the possibility of applying them to various special practical questions, and may be found in courses on hydrodynamics (for example, in Lamb’s Hydrodynamique, German ed. 1907, p. 86 et seq.).

In § 7 (pp. 21–28) the author considers questions concerning the discharge of the flow, the surfaces of minimum velocity and maximum pressure, and finally gives a graphical determination of the pressure and of the energy expended.

In § 8 (pp. 28–44) various forms of draft tubes are considered, depending on the conditions of diverting water away from the turbine wheel. Here the author applies Prasil’s method for determining the form of the draft tube by separating from the flow a certain definite bundle of streamlines in order to obtain various tube shapes, including shapes that are not symmetrical with respect to the axis of the flow. Considering in this way the discharge of water into a basin of finite depth with two flat vertical side walls meeting at an angle, he obtains the form of the bent concrete tubes most widely used at the present time.

But although the author thereby obtains a form of draft tube similar to the concrete tube now used in practice, the application in this case of Prasil’s method for obtaining it is hardly admissible at all, for the following reason: Prasil, considering the motion of the fluid upon leaving the runner—

does not impose any constraint when deriving the shape of its pipe; the liquid flows out of the wheel symmetrically with respect to the axis of the wheel and continues to flow farther in its pipe likewise symmetrically, without in the least disturbing the state of velocities, pressures, and so forth, established at the outlet from the wheel; in this case the pipe is, as it were, the natural continuation of the wheel rims; but not so with Mr. Milovich: here we must suppose that the eccentric discharge of water from the wheel in no way disturbs the form of the flow established at the outlet from the wheel; only then, of course, can we obtain the streamlines, surfaces of equal velocities, pressures, and so forth, the same as in the symmetric flow of the liquid; such an assumption, however, is based on nothing.

Although the author also introduces an intermediate link between the wheel and the bent part of the pipe—a cylindrical pipe—he again does this without proper grounds; it is important to show theoretically what role this part of the pipe will play, how large it should be, and whether in general it is capable of smoothing the transition of the water from the wheel to the bent part; this has not been done by the author, and with it the justification for deriving the given shape of the pipe is also lost.

In an analogous manner the author derives the shape of a pipe for discharging liquid into a basin of finite depth with two and three plane vertical walls, in the case of two parallel ones.

The desire to protect the suction pipe from the possibility of a lowering of its suction action, owing to the condition under which water flows out of it, leads him, quite rightly, to the idea of providing the suction pipe with a diffuser. But, referring to the present absence of a theory of the motion of water from channels of a definite width into wider ones, he gives no direct answers to the question of the shape of this diffuser, contenting himself only with certain general indications concerning the magnitude of the pressure in the most constricted part of this diffuser.

In § 9 (pp. 44–47) the author determines the position of the bottom of the suction pipe relative to the horizon of the lower water, taking as the limiting height of the lower level above the horizontal plane of the origin of coordinates the height above it of the points of minimum velocity on the highest jet of the pipe profile, and then returns to the shape of the diffuser of the pipe, assuming the horizon of the lower water to be variable; in doing so, the author not only gives no definite and direct solution of the question, but also makes an error in supposing that the form of the flow into a funnel is identical with the form of the flow out of a funnel.

In § 10 (pp. 47–55), the author, proceeding from the proposition that the assumption made above—that the outflow of water from the wheel channels is strictly normal to the outlet surface—never actually occurs, considers two rotational motions of a fluid: non-vortical (already studied by Prasil; see Schweiz. Bauz. 1903, No. 25, p. 283) and vortical, in which the vortex lines coincide with the streamlines, and arrives, on the one hand, at the conclusion that in the suction pipe the motion of the fluid should be closer to the latter than to the former, and, on the other, that the rotational “motion of the fluid near the axial part of the pipe has a harmful influence on the operation of the turbine wheel,” a conclusion which Prasil had already reached (ibid.).

Finally, in § 11 (pp. 55–58), the author points out the analogy between the shape of the suction pipe and the shapes of a horn.

Turning now to a general characterization of Mr. Milovich’s works, I, leaving aside his first article, “Outlining the Blades of a Francis Turbine by Pfarr’s Method,” as not having, in my opinion, any particular scientific significance, shall dwell only on the second work, “An Essay in the Theory of the Suction Pipe.” This work, which is a reworking of Prasil’s work, although it treats the question more broadly than that scholar considered it, does not always possess a rigorous substantiation of its conclusions; the author, while criticizing the practical applicability of Prasil’s pipe, whose method he himself uses, does not offer in exchange a pipe that would satisfy all the theoretical conditions of the flow of fluid through it; the question of the flaring of the pipe is not resolved to a sufficient degree.

But at the same time the work shows that the author strove independently and conscientiously to develop certain questions connected with the theory of the suction pipe, that he has a free command of scientific language and knows how to handle mathematical analysis. I am convinced that, in time, with the same attitude toward the task, Mr. Milovich will succeed in overcoming the difficulties of the questions he is developing and in making a valuable contribution to science. The necessity, recognized by him himself, of experimental verification of theoretical results will serve as a guarantee of a correct understanding of the subject and will protect him from excessive infatuation with theory.

Tomsk, January 1908.

V. Pinetgin.

1. Pfarr. Die Turbinen für Wasserbetrieb 1907, p. 214 ff. ↩↩

2. Ibid., p. 215. ↩↩