# Hydraulic integrator Lukyanova

Computer, but not electric.
Hydrointegrator - hydraulic calculator:

Water flowing from one glass tube to another made it possible to solve partial differential equations.

It was during the period of industrialization of the USSR, when a freshly baked engineer Vladimir Lukyanov fell on the construction of the railway and faced the problem of poor quality concreting (when cracking, concrete cracked). Lukyanov suggested that this is due to temperature stresses and summarized the existing theoretical developments. The process was described by differential equations requiring lengthy calculations, but Lukyanov saw the main thing - the analogy between the equations describing heat transfer and the equations describing the fluid flow. Those. the first process could be modeled using the second.

A few years later, Lukyanov creates an apparatus for solving this very specific problem - analyzing the temperature change in concrete depending on its composition, pouring technology and environmental conditions.

##### An example of a problem being solved

Heat transfer under non-stationary conditions - cooling of a multilayer flat wall.

The model is assembled from a series of cylindrical vessels connected in series by calibrated tubes. Each of the vessels imitates the heat content of the wall layer into which the studied fence is divided. The vessels are filled with water to levels corresponding to the initial temperature in each of the layers, after which taps open, and water begins to flow from the vessels. The change in water levels in the vessels will be similar to the change in temperature in the corresponding layers of the wall when it is cooled.

The following analogies were used with the thermotechnical parameters of the enclosing structures under study:
a) the water levels in the vessels in cm correspond to the differences in temperature of the layers and air in degrees;
b) the cross-sectional area of ​​the vessels in cm correspond to the specific heat of the layers in kcal / degree;
c) the amount of water in the vessels in cm corresponds to the heat content of the layers in kcal;
d) the hydraulic resistances of the tubes in min / cm (?) connecting the vessels to each other correspond to the thermal resistances of the layers in deg-h / kcal;
d) the hydraulic resistance at the outlet tube corresponds to the resistance to heat transfer from the wall surface to the air in deg-h / kcal;
f) the water flow rate in cm / min corresponds to the heat flux in kcal / h.
The time scale, i.e., the ratio of the actual duration of the heat transfer process in hours to the duration of the process on the hydraulic integrator in minutes, is equal to the product of the ratio of heat capacity to the cross-sectional area of ​​the vessel and the ratio of thermal resistance and hydraulic resistance.

For the possibility of fixing temperatures (water levels in vessels) at certain points in time, the hydraulic integrator had a special device that simultaneously closed all the taps between the vessels. At this point, it was necessary to note on graph paper located behind the tubes, the water levels in the piezometers. Then the cranes were opened, and so on until the next measurement. The resulting curve was a solution to the equation.

In other words, the integrator made it possible to replace the process, direct observation of which is difficult, with a similar, but more visual process. Moreover, it is important that both processes are described by the same mathematical dependencies.

##### The fate of the project

Strange as it may seem, this did not end there. Engineer V.S. Lukyanov eventually became a doctor of technical sciences and received the Stalin Prize. He designed two-dimensional and three-dimensional hydraulic integrators in the form of standard unified blocks, which could be assembled depending on the problem being solved. Moreover - hydraulic integrators were launched into serial production. It was with their help, in particular, that the projects of the Karakum Canal, the Baikal-Amur Railway, the world's first hydroelectric power station from precast concrete - Saratov, were calculated. They were used in geology (groundwater movement), metallurgy (cooling of castings), rocket science, etc.

Two Lukyanov hydraulic integrators are presented in the collection of analog machines of the Moscow Polytechnical Museum. One of them:

Photograph taken at the Polytechnic Museum

1. Article in "Science and Life" .
2. Fokin K.F. Construction heat engineering of enclosing parts of buildings .