Bernoulli's Law

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Bernoulli's Law

(After Daniel Bernoulli, 1700-1782, Swiss scientist).
1. In aeronautics, a law or theorem stating that in a flow of incompressible fluid the sum of the static pressure and the dynamic pressure along a streamline is constant if gravity and frictional effects are disregarded.
From this law it follows that where there is a velocity increase in a fluid flow there must be a corresponding pressure decrease. Thus an airfoil, by increasing the velocity of the flow over its upper surface, derives lift from the decreased pressure.
2. As originally formulated, a statement of the conservation of energy (per unit mass) for a nonviscous fluid in steady motion. The specific energy is composed of the kinetic energy u2/2, where u is the speed of the fluid; the potential energy gz, where g is the acceleration of gravity and z is the height above an arbitrary reference level; and the work done by the pressure forces of a compressible fluid Missing Image:IMG height=18 src="equat/integral.gif" width=7 v dp, where p is the pressure, v is the specific volume, and the integration is always with respect to values of p and v on the same parcel. Thus, the relationship

Missing Image:IMG align=center height=40


width=108 = Constant along a streamline

is valid for a

compressible fluid in steady motion, since the streamline is also the path. If the motion is also irrotational, the same constant holds for the entire fluid.


This article is based on NASA's Dictionary of Technical Terms for Aerospace Use