Blaise Pascal in the 1600s contributed some of the initial theory to this field. But the term originates from the work of Daniel Bernoulli, it is based on the title of his work called Hydrodynamica (1738). He worked with Leonhard Euler, and they established the general equations of hydrodynamics.
The practice was continued by people such as Joseph Louis Lagrange (1736-1813) with the Euler-Lagrange system, Jean le Rond d'Alembert (1717-1783) discovered the Cauchy-Riemann equations , Pierre Simon Laplace (1749-1827) with the governing equation in the potential flow named after him, Hermann Ludwig Ferdinand von Helmholtz (1821-1894) and William Thomson, Lord Kelvin (1824-1907) with Kelvin-Helmholtz instability (see also Rayleigh-Taylor and Richtmyer-Meshkov) as well as Helmholtz's work on vortices.
See also