Bernoulli Equation


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Bernoulli equation

[ber‚nü·lē i′kwā·zhən]
(fluid mechanics)
Bernoulli theorem
(mathematics)
A nonlinear first-order differential equation of the form (dy / dx) + yf (x) = yng (x), where n is a number different from unity and f and g are given functions. Also known as Bernoulli differential equation.

Bernoulli Equation

 

a differential equation of the first order of the form

dy/dx + Py = Qyα

where P and Q are predetermined continuous functions of x and α is a constant. With the introduction of the new function z = y-α + 1, the Bernoulli equation is reduced to a linear differential equation with respect to z. The Bernoulli equation was considered by Jakob Bernoulli in 1695, and a method of solving it was published by Johann Bernoulli in 1697.

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