Bernoulli Equation

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Bernoulli equation

[ber‚nü·lē i′kwā·zhən]
(fluid mechanics)
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Furthermore, if (5) are selected for some different forms, such as the Riccati equation, Bernoulli equation, and Jacobi elliptic equation, then different exact solutions for (2) can be obtained correspondingly.
Correlation between wind velocity and pressure is governed by the Bernoulli equation as shown in Equations 4 and 5 (Jung 2014).
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 artery pressure (sPAP) over tricuspid regurgitation was calculated with the modified Bernoulli equation formula with a sector probe (P17/1-5 MHz, Sonosite Inc.).
The unsteady Bernoulli equation is employed for evaluating of time historical of the velocity potential and can be written as:
According to the Bernoulli equation (which can also help explain how airplanes stay aloft), each vortex is therefore a region with low pressure, or suction.
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.
Hristov, "An exercise with the He's variation iteration method to a fractional Bernoulli equation arising in a transient conduction with a non-linear boundary heat flux," International Review of Chemical Engineering, vol.
It covers fluid statics; elementary fluid dynamics and the Bernoulli equation; fluid kinematics; finite control volume analysis; differential analysis of fluid flow; dimensional analysis, similitude, and modeling; viscous flow in pipes; flow over immersed bodies; open-channel flow; compressible flow; and turbomachines.
* 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., 2006):