define the bernoulis theorem

Bernoulli theorem:When a non viscous , incompressible fluid flows steadily through a tube of varying cross section ,then the sum of pressure energy, potential energy and kinetic energy remains constant per unit volume about any point in its flow

In compressible,non viscos ,study fluid following into tube the total work done per unit volume is equal to sum of change in kinetic energy and potential energy is constant per unit volume.

Full Definition of BERNOULLI`S THEOREM 1 [after Jacques Bernoulli] : a basic principle of statistics: as the number of independent trials of an event of theoretical probability p is indefinitely increased, the observed ratio of actual occurrences of the event to total trials approaches p as a limit —called also law of averages 2 [after Daniel Bernoulli] : a law of hydrodynamics: in a stream of liquid the sum of the elevation head, the pressure head, and the velocity head remains constant along any line of flow provided no work is done by or upon the liquid in the course of its flow and decreases in proportion to the energy lost in viscous flow.

WHEN a non-viscous incompressible fluid flows steadily in a tube varying cross sections , the sum of pressure energy , kinetic energy, potential energy per unit area remains constant at any point in its flow.

When a non-viscous incompressible fluid flows steadily in a tube varying cross sections , the sum of pressure energy ,kinetic energy , per unit area remains constant at any point in its flows.

it states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit length that occur during the flow

An idealized algebraic relation between pressure, velocity, and elevation for flow of an inviscid fluid. Its most commonly used form is for steady flow of an incompressible fluid, and is given by the

equation below, where p is pressure, ? is fluid density (assumed constant), V is flow velocity, g is the acceleration of gravity and z is the elevation of the fluid particle. The relation applies along any particular streamline of the flow. The constant may vary across streamlines unless it can be further shown that the fluid has zero local angular velocity.

The above equation may be extended to steady compressible flow (where changes in ? are important) by adding the internal energy per unit mass, e, to the left-hand side.

The equation is limited to inviscid flows with no heat transfer, shaft work, or shear work. Although no real fluid truly meets these conditions, the relation is quite accurate in free-flow or “core” regions away from solid boundaries or wavy interfaces, especially for gases and light liquids. Thus Bernoulli's theorem is commonly used to analyze flow outside the boundary layer, flow in supersonic nozzles, flow over airfoils, and many other practical problems.

In fluid dynamics, Bernoulli`s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid`s potential energy. ...

FOR A INCOMPRESSIBLE, NON VISCOUS,STEADY FLOW OF FLUIDS THE SM OF KINETIC ENERGY,POTENTIAL ENERGY AND PRESSURE ENERGY ARE CONSTANT PER UNIT VOLUME OF THE FLUID REMAINS CONSTANT AT ALL POINTS IN THE PATH OF THE FLOW.