Bernoulli equation and its physical applications
The Bernoulli equation has the form
 |
(1) |
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
 |
(2) |
The substitution
 |
(3) |
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).
- 1
- N. PISKUNOV: Diferentsiaal- ja integraalarvutus kõrgematele tehnilistele õppeasutustele. - Kirjastus Valgus, Tallinn (1966).
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