If you walked up to someone today and asked what types of computers there were out there: they would probably wonder if you were referring to the differences between a desktop, laptop, and maybe something like a Raspberry Pi. Or even a quantum or optical/photonic computer.
But as the rich and diverse history of computing shows: a computer can be made from practically anything. As has been seen with mechanical, fluidic/flueric, biological, and many other systems.
For this post, however, I will give some very interesting insights into the Hydraulic Computer and its amazing, yet largely unknown history. As it is a device that should be deeply reconsidered for implementation in the modern day.
The First Hydraulic Computer
The first known modern Hydraulic Computer was created in the 1890s by Mihailo Petrovic of Serbia for the solution of First-Order Ordinary Differential Equations (ODEs)   . At the time: the device sparked a good amount of interest in the scientific community   , but was not further developed by Mr. Petrovic; as he was more concerned with researching differential equations and mathematical analogs to natural phenomena than developing machines  .
Independent of this research: Dimitri Budrin created a hydraulic computer, known as the Hydrointegrator, in 1932 at the Urals Institute of Steel in the U.S.S.R. . Another engineer, Vladimir S. Lukyanov, had also developed a similar device at the People's Commissariat of Transport of the USSR (CNIIS) for calculating the expansion and contraction of soil in permafrost regions for the development of railroads in those regions . These two engineers soon began to collaborate together on the Hydrointegrator  and its development in various fields.
The Hydraulic integrator was used in the Soviet Union from the early 1930s to the 1980s. It was used to calculate mainly diffusion-type Partial Differential Equations in the fields of mining, metallurgy, geology, civil engineering, and rocket science  . For further information on the Hydro-Integrator: I have included a list of patents at the bottom of this article.
This device uses what is known as the Finite Difference Method to represent multiple sections or layers of a material across a given span by multiple standpipes and valves. These compnents are then adjusted individually to represent the various values of the material(s) being simulated  . The hydraulic resistance of each section was adjusted by either twisting a special adjustable capilary tube, or simply using a valve that could readily have its value dialed in. The cross-sectional area of the standpipes were adjusted by either using pipes with different diameters, or immersing rectangular strips of metal into the pipe  .
The Hydrointegrator works by exploiting the nearly identical similarity between Darcy's Law of fluid flow through porous media and Fouier's Law of heat conduction in one-dimension  . These laws are then transformed to form difference equations which can then be simulated by the apparatus by representing the rate of heat conduction by the rate of water flow, the amount of heat in a given section of material by the amount of water in a standpipe, the heat capicity of the material by the cross-sectional area of the standpipe, and the thermal resistance of the material by the hydraulic resistance of the valves , adjustable capillary tubes , etc. that is placed between each standpipe.
The Hydraulic Integrator could be extended into different fields by simply substituting the unit to be measured for its hydraulic analog and modifying portions of the device for factors that are unique to the type of problem being solved for (such as additional reservoirs placed atop the first few standpipes in the apparatus to simulate the effects of latent heat when calculating the freezing and thawing of soils  .
In the present: two surviving Hydraulic Integrators can be found at the Polytechnic Museum in Moscow, Russia .
Another coincidental creation of a hydraulic computer came in 1935, when Dr. Arthur D. Moore of the University of Michigan created a very similar apparatus known as the 'Hydrocal'  ; with its name lending to the fact that it was originally designed for the simulation of chemical reactions . This device was very much like the Hydro-Integrator, except that it featured a plugboard-like panel for re-arranging the connections between tubes. As well as a board that all of the tubes in the device were affixed to, so that the cross-sectional areas of the tubes could be modified by changing the angle of the board .
Unfortunately, however, Dr. Moore's invention suffered from several flaws and was abandoned by him a few years later.
The Hydraulic Integrator Developed at MIT
In 1947, inspired by the works of V. S. Lukyanov and A. D. Moore: professors Harl P. Aldrich and Henry M. Paynter, as well as Robert F. Scott and other students, of the Massechusets Institute of Technology (MIT) had designed and constructed a functional Hydraulic Integrator for the solution of heat transfer in multi-layered soils in 1-dimension .
This second integrator was part of a contract between MIT (via the Division of Industrial Cooperation(DIC Project No. 5-7155 ))  and the Artic Construction and Frost Effects Laboratory (ACFEL) of the New England Division of the US Army Corps of Engineers (USACE) was launched to evaluate the performance and feasibility of using the Hydraulic Integrator for the computation of freezing and thawing in soils in permafrost regions       .
The device ( best illustrated in the ACFEL Technical Reports 42 and 62, as well as CRREL Technical Report #135    ) was relatively simple in its design and construction, consisting mainly of vertical glass tubes connected together by adjustable capillary tubes , as well as several reservoirs which simulated the presence of latent heat in the system . The design itself was essentially a stripped-down version of the Lukyanov Hydraulic Integrator (missing instruments like flowmeters, dial-adjusted resistors, prismatic metal inserts, etc.), with the exception of an electromechanically actuated 'Programmer' device that was used to automatically adjust the height of the reservoir that supplied water to the rest of the apparatus  .
According to Technical Report 62: the inaccuracy of the results obtained from the device was found to be negligible when the solutions are programmed as per the procedure given in chapter 4 of 'Design and Operation of an Hydraulic Analog Computer for Studies of Freezing and Thawing of Soils' [16 - page 36] . This same conclusion was also reached in ACFEL Technical Report 67 .
In 1963: the error of the Hydraulic Analog Computer was also found to be low by by Rhoderick Hawk and William Lamb in their study of the heat flow through typical walls found in buildings . They reported that the average error returned by the computer was 3.2%; although several of the errors were due to the function of the Programmer, which would fail to run at a constant speed; and the cam for the input curve would slightly slip during its operation.
Currently it is unknown exactly why the project, although being a success, wasn't further developed and extended into fields outside of civil engineering; but some of the reports indicate that the device was very tedious reconfigure between experiments, as each resistor and standpipe needed to be manually re-adjusted. However, the most likely factor that stopped the proliferation of the Hydraulic Computer in the United States: was the advancement of the electronic analog and digital computers that were far easier to operate and could be rapidly reconfigured to solve problems that were outside the reach of hydraulic computers at that time.
Both the blueprints and operation instructions can be found in 'Design and Operation of an Hydraulic Analog Computer for Studies of Freezing and Thawing of Soils'  for those interested in creating a replica of the device.
Other Hydraulic Computers
Throughout the rest of the 20th Century, a few other hydraulic computers were occasionally produced by various inventors. A few are mentioned here.
In 1957: two Czechoslovakian nationals, Alois Polangski and Mirko Hruby, filed a patent titled 'Hydromechanical Model' . Which was an apparent improvement over the 'Hydrocal' designed by Arthur D. Moore. The device (US Patent 2903186 ) is very simiar to the one developed at MIT, in that an electronic controller is used for the Programmer, but features an improved setup that allows two programmers on either side of the device to interact with each other . Nothing aside from the patent can be found on either the device or its inventors.
Another, apparently indepent, invention of a hydraulic computer: occured in 1964 in Austrailia by H. A. Scholer of the Sydney Department of Public Works . The device was built to simulate the flow of surface water through the Howes Lagoon drainage area in New South Wales, Australia. The device works in a very simar manner to the other hydraulic computers (with the exception of M. Petrovic's device); with the exception that the interconnected reservoirs of water in the device are to represent specific bodies of water (namely lagoons), while the interconnecting pipes and valves represent the hydraulic resistance of the tributaries and rivers that interconnect the different bodies of water.
The most recent, and most versatile, invention of a hydraulic computer: is the Multi-Purpose Fluid Analog Computer developed by Parviz Monadjemi at Shiraz University in Iran in 2001 . The computer features several improvements over the previous computers, including the ability to use feedback by connecting the standpipes/reservoirs at the tops of the containers (causing the air in one reservoir to interact with the air in either the other reservoirs or with the atmosphere), as well as produce various non-linear functions by using differently shaped reservoirs. The device functions in a very similar way to the Lukyanov Hydrointegrator; and can be used to solve diffusion type partial differential equations up to three dimensions by employing the very same techniques as the Hydrointegrator   . The main difference between this apparatus and the previous ones: is that tubes filled with porous rock are used in place of valves or adjustable capillary tubes for the hydraulic resistance , as the apparatus was mainly used in Hydrology for studying the flow of groundwater  .
The hydraulic computer is a very interesting and surprisingly accurate way to compute the solutions to a variety of different diffusion-type partial differential equations; and could possibly even be modified, using feedback, to handle elliptic partial differential equations (such as the Wave Equation). Although a technology such as this may be of little use for modern industry and computation: it presents a potentially powerful and highly available means for creating computation and control systems for the Developing World.
Some of V. S. Lukyanov's Patents: (can be found at PatentDB.su)
SU 41730, SU 43763, SU 44065, SU 49508
Other (Russian) Hydraulic Integrator Patents:
SU 1273032 Golub -- Hydraulic Integrator (1984), SU 974974 Hydraulic Integrator (1980), SU 808856 Hydraulic Integrator (1979), SU 1016680 Hydraulic Integrator (1983), SU 96947 Hydraulic Integrator (1954),
 W. A. Price, (1900), Petrovitch’s Apparatus for integrating Differential Equations of the First Order, The London,
Dublin, and Edinburgh Philosophical Magazine and Journal of Science, Taylor & Francis, 1900, Vol. 49
 Petrovitch, M. M.. (1900). Appareil a Liquide pour L'Intégration Graphique de Certains Types D'Équations
Différentielles. American Journal of Mathematics, 22(1), 1–12. http://doi.org/10.2307/2369763
 A. D. Moore (1936), The Hydrocal, A Hydrodynamic Calculating Machine for Solving Unsteady-State Problems in Heat Transfer and Other Types of Diffusion, Industrial and Engineering Chemistry, Vol. 28, No. 6, pp. 704-708
 V. S. Lukyanov (1939), Hydraulic Apparatus for Engineering Computations, (Translation) MIT, US Army Corps of Engineers - New England Division, Arctic Construction and Frost Effects Laboratory (1955)
 H. P. Aldrich, H. M. Paynter (1953), Analytical Studies of Freezing and Thawing of Soils, US Army Corps of Engineers - New England Division, Artic Construction and Frost Effects Research Laboratory, Massechusets Institute of Technology - Department of Civil and Sanitary Engineering, Report No. 42
 H. P. Aldrich, R. F. Scott, G. L. Leung, R. S. Nordal (1956), Design and Operation of an Hydraulic Analog Computer for Studies of Freezing and Thawing of Soils, US Army Corps of Engineers - New England Division, Artic Construction and Frost Effects Research Laboratory, Massechusets Institute of Technology - Department of Civil and Sanitary Engineering, Report No. 62
 R. F. Scott (1961), Heat Transfer at the Air-Ground Interface with Special Refernce to Airfield Pavements, US Army Corps of Engineers - New England Division, Artic Construction and Frost Effects Research Laboratory, Massechusets Institute of Technology - Department of Civil and Sanitary Engineering, Report No. 63
 H. P. Aldrich, R. S. Nordal (1957) Frost Penetration in Multi-Layer Soil Profiles, US Army Corps of Engineers - New England Division, Artic Construction and Frost Effects Research Laboratory, Massechusets Institute of Technology - Department of Civil and Sanitary Engineering, Report No. 67
 A. C. Rigas (1951), The Consolidation Analogy Model, Mass. Inst. of Technology, S. B. Thesis
Sources of Images
 [p. 487] W. A. Price, (1900), Petrovitch’s Apparatus for integrating Differential Equations of the First Order, The London,
Dublin, and Edinburgh Philosophical Magazine and Journal of Science, Taylor & Francis, 1900, Vol. 49
 [p. 706] A. D. Moore (1936), The Hydrocal, A Hydrodynamic Calculating Machine for Solving Unsteady-State Problems in Heat Transfer and Other Types of Diffusion, Industrial and Engineering Chemistry, Vol. 28, No. 6.
 [p. 62] H. P. Aldrich, R. F. Scott, G. L. Leung, R. S. Nordal (1956), Design and Operation of an Hydraulic Analog Computer for Studies of Freezing and Thawing of Soils, US Army Corps of Engineers - New England Division, Artic Construction and Frost Effects Research Laboratory, Massechusets Institute of Technology - Department of Civil and Sanitary Engineering, Report No. 62
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