The issues of work and pressure during rolling, obviously related to one another, have long been the subject of research, both theoretical and experimental. The number of large experimental studies devoted to these issues is small. For my part, I will dwell only on those conclusions of other researchers that the course of my research leads me to consider (see article). Kodron's theoretical research was accompanied by laboratory experiments on rolling lead bars between rollers of small diameter. I will dwell somewhat on these experiments in the future, since it was these experiments that first of all gave me the opportunity to verify the correctness of the theoretical formulas I had derived.
To check to what extent the calculations using the formulas I derived in previous notes are consistent with the experimental results, I, but on the instructions of Prof. I. A. Thieme applied these formulas to the data of experiments carried out on the rolling of sheet iron at the Schulz, Knaudt, etc. plant. C° in Essen. These data are presented in the article by Prof. Thieme: “Indicative experiments on rolling steel rails and beams” (Mining Journal, 1883) and in the article by E. Blass: “Zur Theorie des Walzprocesses” (Stahl u. Eisen, 1882, No. 7).
In this note, I aim to find the dependence of the pressure per unit surface of a metal compressed between two parallel planes on the thickness of the compressed piece of metal, considering other conditions equal. The reason that determines the dependence of the pressure per unit surface on the thickness of the compressed piece of metal is that during compression the associated increase in the transverse dimensions of the compressed piece, and therefore the area of contact of the metal with the compressive planes, a friction force arises between the compressed metal and the compressive planes . Let us now study the influence of this force (see article).
Let us denote by r the radius of the roll and by φ the angle through which the roll has turned over a certain period of time. We can imagine the rolling process in such a way that the rolled end of a metal bar remains motionless, and the rollers roll along the surface of the bar (see article).
The question of the form of a free jet when a perfect liquid flows out of a vessel, when the movement occurs in a plane, was first solved by Helmholtz for the case of liquid flow through a channel protruding into this vessel. Helmholtz’s method was then generalized by Kirchhoff, who gave a solution to several problems related to plane the movement of a fluid, and, by the way, the problem of the flow of fluid through a slot in a flat wall.Both of these problems are considered by Lamb in his treatise on hydrodynamics, and he uses the method of conformal transformations of Schwartz and Christoffel to derive the equation of a free jet. The purpose of my present note is to apply the same method to the derivation of the equation of a free jet when a liquid flows through a hole in a vessel with flat walls, and the walls converge to the hole at an angle of 2a.
