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.

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 It might be outdated or ideologically biased.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 = Qy^α

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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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.

Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method

Correlation between wind velocity and pressure is governed by the Bernoulli equation as shown in Equations 4 and 5 (Jung 2014).

Infiltration and heating load analysis of an apartment with respect to window type, window location, and lock operation

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):

Dynamic performance of air spring based on SIMPACK and Matlab Simulik joint simulation

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.).

Effectiveness of thoracic ultrasonography in the evaluation of the severity of pulmonary involvement in patients with systemic sclerosis

The unsteady Bernoulli equation is employed for evaluating of time historical of the velocity potential and can be written as:

Numerical study on a bubble dynamic generated by ultrasound waves in liquid-saturated porous media

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.

Seal whiskers inspire marine technology: by closely observing nature, biomimetic engineer designs a new sensor

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.

The frequency of pulmonary hypertension in patients with juvenile scleroderma

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.

Fluid dynamics

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.

Local fractional Laplace variational iteration method for solving linear partial differential equations with local fractional derivative

The Bernoulli equation we consider in this paper is

New exact solutions for a higher-order wave equation of KdV type using the multiple simplest equation method

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.

Fundamentals of fluid mechanics, 6th ed. (online access included)

* 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):

Arm position simulation of PAM based actuator