In 1936 Vladimir Lukyanov built a water computer that was the world's first computer for solving (partial) differential equations. The operator solved the equations by "playing around" with a series of interconnected tubes filled with water.
According to an article in Wikipedia this type of analog computer called a Water Integrator was built in the Soviet Union as far back as 1928. According to that article the water levels in the various chambers represented stored numbers. The rate of flow between tubes represented mathematical operations. These water computers were used in the USSR for large scale modeling right up into the 1980's when digital computers became more sophisticated.
An article published in the Russian magazine Science and Life in 2000 called the Lukyanov computer one of the monuments of science and technology and claimed that it brought the Soviet Union to the forefront of the development of the analog computer.
Lukyanov's computer was built for the particular purpose of solving the practical problem of cracking in concrete. To solve the cracking problem involved calculating the complex relationships between the material properties of the concrete, the curing process, and environmental conditions. Whereas existing calculation methods did not give quick or accurate solutions, the Lukyanov water computer did. An article here describes the process:You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the production line of concrete blocks. It lets you see (literally) what would happen if you change the type of cement used or increase the load capacity of the concrete or whatever; just open a valve here or pull a lever there and the machine sloshes away, showing in real time how the water levels rise and fall in various tanks representing material properties, curing time, temperature, and so on. Changes to levels were plotted on graph paper.
These water computers were used successfully in other areas such as geology, metallurgy, thermal physics, and rocket engineering. In the 1970's these computers were still used in 115 manufacturing, research, and educational institutions in the USSR. It was not until the 1980s that digital computers came to surpass the functionality of the "hydraulic integrator" or water computer.