In the history of computing, the 1930s marked a pivotal era. As the world grappled with the Great Depression and the looming threat of another global conflict, scientists and engineers sought new tools to tackle increasingly complex mathematical problems in fields like physics, engineering, and military technology.
It was against this backdrop that a young Soviet engineer named Vladimir Sergeevich Lukianov conceived of a radically new type of computing device – one that used water instead of gears, levers, or electricity to perform calculations. His "hydraulic integrator," developed in 1934, was the first working "water computer" and an important early milestone in analog computing.
The Thermodynamics Problem
Lukianov was born in 1902 in Moscow and graduated from the Moscow State University of Railway Engineering in 1925. After working on railway construction projects for several years, he took a research position at the Central Institute of Railway Engineers in Moscow in 1930. There, he grappled with the challenge of calculating temperature dynamics in large concrete structures.
This was a critical problem for civil engineering in the Soviet Union at the time. Massive concrete structures like railway bridges, dams, factories, and military fortifications were key to the USSR‘s industrialization and infrastructure development plans under Joseph Stalin. However, the country‘s harsh climate posed challenges. Improperly managed thermal stresses from seasonal freezing and thawing could crack or damage concrete, with potentially catastrophic consequences.
As Lukianov noted in a 1940 paper, the mathematical modeling of thermodynamics in concrete was a "complex and as yet unresolved problem" that required solving unwieldy differential equations. Conventional calculation methods were slow, cumbersome, and relied on simplifying assumptions. A faster and more accurate solution was needed.
The Hydraulic Integrator
Lukianov‘s insight was to view the problem in terms of flows between interconnected vessels – similar to the way heat flows through a solid material. By constructing a physical model of the equations using water, he could simulate the dynamics in realtime and extract the solutions from the changing water levels.
He presented the first prototype of his hydraulic integrator, designated ИГ1 (Integrator Gidravlicheskiy 1), in 1934. The device consisted of a series of interconnected glass vessels and tubes mounted on a panel, with valves to control the flow between them. Each vessel represented a point in the structure being modeled, and the water level corresponded to the temperature at that point.
Here is a simplified diagram of the basic configuration:
++
 
 Main  Adjustable
 Vessel  Flow Valve
   
Initial ++  +++
Water Flow +) 
>  +++
++  
   Piezometer Tube
 Vessel 2  
  +++
++  
++
 Water Out 
++
To model a specific problem, the operator would configure the initial water levels in the vessels and the positions of the valves based on the boundary conditions and material properties. They would then use a predefined schedule to adjust the valve positions over time, simulating the changing thermal conditions. Meanwhile, the water levels in the piezometer tubes would be recorded on graph paper at regular intervals, plotting out the temperature curves.
Through this elegant hydraulic simulation, Lukianov‘s device could provide a continuous, realtime "computation" of the thermal dynamics described by the underlying differential equations. It was a powerful new tool for investigating previously intractable thermodynamics problems.
Global Reception
Lukianov continued refining his invention through the 1930s and 40s, building multidimensional integrators and extending the technique to other engineering domains. He received a patent for the device in 1936 and published several papers detailing its construction and applications.
The global scientific community took notice. In 1938, the German applied mathematician Irmgard FlüggeLotz constructed her own version of the hydraulic integrator at Stanford University and used it to solve aircraft design problems. An American researcher, John Stancliffe, published an influential paper on "fluid mappers" in 1944, citing Lukianov‘s work.
In the Soviet Union, the hydraulic integrator was hailed as a breakthrough. In 1943, the journal Hydraulics and Sanitary Engineering reported:
"The hydraulic integrator, originated by Engineer V. S. Lukianov, is the latest achievement of Soviet science in the field of applied mathematics… With the aid of this device, it is possible to solve a wide variety of problems whose mathematical formulation reduces to linear partial differential equations."
Production and Practical Applications
After World War II, the Soviet government ramped up production of the devices. In 1949, the Moscow Plant of Calculating Machines (SAM) began manufacturing standardized hydraulic integrators, designated ИГ2, ИГ3, and so on. By the mid1950s, they were being used in dozens of Soviet research institutes, engineering bureaus, and universities.
Some notable applications included:

Dam Construction: Hydraulic integrators were used to model the thermal stresses in several large Soviet hydroelectric projects in the 1950s, including the Kuibyshev Dam on the Volga River and the Bratsk Dam in Siberia. By optimizing the concrete pouring and cooling schedules, engineers could minimize cracking and ensure structural integrity.

Permafrost Engineering: Soviet scientists used hydraulic integrators extensively to model heat transfer in frozen soils, a critical concern for construction in the Arctic regions of Siberia, the Russian Far East, and Central Asia. The devices helped optimize the design of building foundations, oil pipelines, and other infrastructure to cope with permafrost dynamics.

Aerospace Research: At the Zhukovsky Academy of Aeronautics and Astronautics in Moscow, hydraulic integrators were used in the 1950s60s to simulate aerodynamic heating of highspeed aircraft and rocket bodies. The data informed the design of thermal shielding and cooling systems for a variety of Soviet aerospace projects.

Nuclear Power: The Kurchatov Institute of Atomic Energy used a hydraulic integrator to model heat transfer in nuclear reactor cores in the 1950s. The simulations helped optimize the design of coolant flows and control rod configurations for enhanced safety and efficiency.
Advantages and Limitations
The key advantages of the hydraulic integrator were its simplicity, reliability, and visual nature. As an analog device, it could provide an intuitive, realtime simulation of physical phenomena governed by differential equations. The water flows were inherently smooth and continuous, mirroring the real behavior of heat transfer and other dynamic processes.
Compared to digital computers of the early Cold War era, which were large, expensive, and unreliable, hydraulic integrators were relatively cheap and easy to maintain. They had few moving parts and could operate for years with minimal servicing. And unlike electronic analog computers, they were largely immune to electromagnetic interference, making them suitable for use in industrial environments.
However, the hydraulic integrator also had some important limitations. Each device could only be configured to solve a specific set of equations determined by the arrangement of vessels and tubes. Changing the problem required physically reconfiguring the machine, a timeconsuming process. The accuracy of the results was limited by the precision of the valve controls and water level measurements, as well as the skill of the human operator.
Moreover, the hydraulic integrator was not a generalpurpose computer. It couldn‘t be programmed to perform arbitrary calculations like a digital computer. Its niche was solving a particular class of partial differential equations common in thermodynamics and fluid dynamics problems.
Lukianov‘s Legacy
Lukianov continued working on hydraulic integrators and other analog computing devices throughout his long career. In 1951, he was awarded the prestigious Stalin Prize for his scientific achievements. He taught at several universities and published numerous papers on hydraulic simulation and modeling.
Even as digital computers began to dominate the computing landscape in the 1960s, hydraulic integrators remained in use in the Soviet Union. As late as 1980, an article in the journal Nature reported that around 40 hydraulic integrators were still in operation across the USSR, used for specialized engineering applications where their particular strengths outweighed the capabilities of digital computers at the time.
Lukianov died in 1980 at the age of 78. His hydraulic integrator, though not as wellknown as other analog computing devices of the era, left an important and enduring legacy. It demonstrated that the principles of analog simulation and computation could be extended beyond the mechanical and electrical domains into the realm of fluids.
As historian Slava Gerovitch argued in a 2008 paper, the hydraulic integrator also embodied a distinctively Soviet approach to computing in the early Cold War era – one that emphasized physical intuition and materiality over the abstract logic of digital computers. In Lukianov‘s device, the data was tangible and visible, the computations played out in realtime before the operator‘s eyes.
Today, Lukianov‘s original hydraulic integrators are preserved in museums in Moscow and St. Petersburg, reminders of a forgotten chapter in the history of computing. In our digital age, it can be hard to imagine a time when a device that sloshed water through glass tubes was the cutting edge of simulation technology. But for Vladimir Lukianov and his contemporaries, the hydraulic integrator was a breakthrough – an elegant, effective tool for probing the boundaries of what was possible with the science of information.