PlanetPhysics/Bernoulli Equation and its Physical Applications

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The Bernoulli equation has the form

where and are continuous real functions and is a constant (, \,).\, Such an equation is got e.g. in examining the motion of a body when the resistance of medium depends on the velocity as The real function can be solved from (1) explicitly.\, To do this, divide first both sides by .\, It yields

The substitution

transforms (2) into which is a linear differential equation of first order.\, When one has obtained its general solution and made in this the substitution (3), then one has solved the Bernoulli equation (1).

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  1. {\sc N. Piskunov:} Diferentsiaal- ja integraalarvutus k\~{o rgematele tehnilistele \~{o}ppeasutustele}. \,-- Kirjastus Valgus, Tallinn (1966).