Introduction to Bernoulli’s equation and It’s Application

The Bernoulli’s equation is one of the most useful equations that is applied in a widevariety of fluid flow related problems.例如，这种等式可以以不同的方式导出，例如，通过将欧拉的方程沿着流线集成，通过将热力学的第一和第二律法应用于稳定，无论是无粘性和可压缩流量等。In simple form the Bernoulli’s equation relates the pressure, velocity and elevationbetween any two points in the flow field.It is ascalar equationand is given by:

IntroductiontoBernoulliE28099sequationandIt27sApplication — 基本Bernoulli的等式

Each term in the above equation hasdimensions of length(i.e., meters in SI units) hence these terms are called aspressure head, velocity head, static headandtotal headsrespectively.

Bernoulli’s equation can also be written in terms of pressures (i.e.,Pascals in SI units) as:

Bernoulli’s equation is valid betweenany two pointsin the flow field when the flow is steady, irrotational, in-viscid and incompressible. The equation is valid along a streamline for rotational, steady and incompressible flows. Between any two points 1 and 2 in the flow field for irrotational flows, the Bernoulli’s equation is written as:

Bernoulli’s equation can also be considered to be analternate statement of conservation of energy (1stlaw of thermodynamics).

Refer this ;Fundamental laws of Thermodynamics

由于所有实际流体都有有限的粘度，即在所有实际的流体流动中，一些能量将在克服摩擦时丢失。这被称为头部损失，即，如果流体在垂直管道上升，则它将上升到较低的高度，而不是Bernoulli方程所预测的。头部损耗将导致流量的压力降低，方程也意味着将一种压力转化为其他形式的可能性。For example,neglecting the pressure changes due to datum, it can be concluded from Bernoulli’s equation that the static pressure rises in the direction of flow in a diffuser while it drops in the direction of flow in case of nozzle due to conversion of velocity pressure into static pressure and vice versa. Figure 1 shows the variation of total, static and velocity pressure for steady, incompressible and inviscid, fluid flow through a pipe of uniform cross-section.方向。如果HEAD损耗由H表示，则伯努利的等式可以修改为：

Fig 1. Application Of Bernoulli Equation.

Figure 1 shows the variation of total, static and velocity pressure for steady, incompressible fluid flow through a pipe of uniform cross-section without viscous effects (solid line) and with viscous effects (dashed lines)

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