Bases of Bernoulli's Equation

Fluid flow past a blunt object will have a stagnation point in front of the body where the velocity is zero. The location of this point has a relatively large pressure and fluid flow divides into two parts, part flowing through the top and another across the bottom of the object.

Bernoulli's equation is an equation may be the most widely used in fluid mechanics. We will obtain Bernoulli's equation and apply them to different schools. Although this equation is one of the oldest in fluid mechanics and the assumptions used in very much lower, these equations can effectively be used to predict and analyze the flow situation. However, if the equation is applied without regard to the precise limits, serious errors can occur. Even this Bernoulli equation equation known as the most widely used and most widely misused in fluid mechanics.

1. Newton's Second Law

If a fluid particle moves from one place to another place, these particles usually experience an acceleration or deceleration. according to Newton's second law of motion, the net force acting on the particles under review should be equal to mass times acceleration: F = ma

Assumption fluid is inviscid, meaning: the fluid is assumed to have zero viscosity. If the viscosity is zero, then the thermal conductivity of the fluid is also zero and no heat transfer will occur (except by way of radiation). In practice there is no inviscid fluid, because in each of the fluid shear stresses arise when it imposed a strain rate of displacement. For most situations, the flow of the viscous effects of relatively small compared to other effects
Inviscid fluid flow is governed by the forces of pressure and gravity.

We assume that the fluid motion governed only by the forces of gravity and pressure and using Newton's second law is set at a fluid particle in the form of:

(net compressive force on a particle) + (net gravitational force on a particle) = (mass of particles) x (particle acceleration)


Fluid particles accelerated in the normal direction and along the stream.
As the particles move, the particle will follow a certain trajectory shape is determined by the speed of these particles. The locus of the particle along the trajectory is a function of where the particle was moving at the beginning and the velocity along the path. If the motion is a steady flow (steady flow), meaning no change according to time at a particular location in the flow field, each successive particles passing through a particular point such as point (1) in the image above will follow the same path. For this case, the path is a fixed line in the xz. Particles passing through adjacent sides of the point (1) will follow his own path, which may differ form the path that passes through the point (2), the entire field filled with xz trajectories were similar.
For steady flow (steady flow), each particle sliding along the trajectory and velocity vectors everywhere tangent to the path is. The lines that are tangent to the velocity vector field of flow around the so-called "flow lines (streamlines). Motion of particles is described in the distance s = s (t), along the line-current from a point of origin that is easy and the radius of local curvature of the line-current, R = R (t). The distance along the flow lines associated with the particle speed V = ds / dt, and the radius of curvature associated with the current form of the line. In addition to the coordinates along the line, s, is also the normal coordinates perpendicular to the flow line, n, as shown in the image above.

To apply Newton's second law on a particle current flowing along the line, we have to write according to the coordinates of the particle acceleration, the current line. By definition, acceleration is the rate of change of velocity with time of the particle, a = dV / dt. For two-dimensional flow in the xz, the acceleration has two components, a component along the line-currents, as the so-called downstream acceleration, and a normal component of flow lines, an, the so-called normal acceleration.

Downstream acceleration comes from the fact that the speed of the particles generally varies along the line-current, V = V (s). For example, in the picture above the rate of these particles may be 100 ft / s at the point (1) and 50 ft / s at the point (2).