Continuum approximation is a famous approximation that is taken in any fluid mechanics textbook. It says that even though the fluid has spaces and voids it can be assumed to behave as a continuous media.
Enter calculus, stage right, which was developed from little "infinitesimals" (generalized atoms.) The result was integral and differential calculus applied to continuous functions (in retrospect, this was an unfortunate choice of terms.) In order to harness the power of calculus, it helps to have a formal underpinning that allows you to treat pressure, density, velocity, and a host of other things you can measure as continuous functions. They didn't have that in the 18th C, but that didn't stop Bernoulli and Euler from applying calculus to fluids. Work, as defined by Coriolis (1826), didn't need calculus, just buckets of water and a rope. But there's only so much you can do with those, and not everyone has a mine shaft. A calculus-based definition of work was a lot more convenient.
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For the special situations where the molecular distance does become important, which is in the order of a billionth of a meter, the continuum model does not apply, and requires statistical techniques to study fluid flow
I believe this answers your question. Fluid on engineering have always been assumed to be continuum fluid until recently. Obviously turbulent flow with a gas mixed with liquid is different because that is a mixture of fluids with different properties. be457b7860
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