Bernoulli Equation


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Bernoulli equation

[ber‚nü·lē i′kwā·zhən]
(fluid mechanics)
(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 + 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.

References in periodicals archive ?
As the contact area with the wall is small when the air flows into the orifice, and the flow rate is fast, so this is regarded as one-dimensional isentropic flow (Liu, 2011), according to the Bernoulli equation, it can be deduced the flow rate at the orifice shrinkage is shown in formula (7):
Systolic pulmonary arterial pressure was calculated by modified Bernoulli equation, in which SPAP = 4 x TRVmax2 + right atrial pressure, where TRVmax was maximal velocity of tricuspid insufficiency.
According to the Bernoulli equation (not discussed in detail here because of space limitations), two gradients exist at the narrowing of the funnel-shaped tube.
Chapter 21 of the 2009 ASHRAE Handbook--Fundamentals, shows how the Bernoulli equation is used to represent airflow through ducts in real systems.
Dependence of pressure in the muscle on muscle volume can be found with help of equation for ideal gases, Boyle-Mariotte law and Bernoulli equation (Kerscher et al.
Chapter 32 of the 1993 ASHRAE Handbook-Fundamentals shows how the basic Bernoulli equation is extended to analyze air flow through ducts in real systems.
Although the practical application of power-balance methods may be limited for lack of measured model parameters, this research has demonstrated that the conventional multizone method is simply a special case of the more general power-balance method with another special case being that based on the generalized Bernoulli equation that is used in the piping network analysis community.
Recovery of the static air pressure, previously [6] considered through a compressible process governed by the Bernoulli equation
The Bernoulli equation is based on the conservation of energy and for open channels is described by
Since there is no single physical location within the plenum at which the absolute pressure is known at this stage of the analysis, the Bernoulli Equation can only be used to establish relative pressures from cell to cell.