In 1718, John Keill challenged the Continental Mathematica, " To find the curve that a projectile may describes in the air, on behalf of the simplest assumption of Bernoulli equation.
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When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock.
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This is the Bernoulli equation for unsteady potential flow, applied at the free surface, and with the pressure above the free surface being a constant which constant pressure is taken equal to zero for simplicity.
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The Bernoulli equation for unsteady potential flow also appears to play a central role in Luke's variational principle, a variational description of free-surface flows using the Lagrangian ( not to be confused with Lagrangian coordinates ).
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I am trying to create a box in which to place a lot of detailed text that is rather inappropriate to the Wiki article itself-very much like the high-powered equations inside the boxes at Bernoulli's principle # Derivations of Bernoulli equation.
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:: Well I was thinking the Bernoulli equation would say conservation of energy means the pressure drops below atmospheric; but wouldn't the movement of the diaphragm contribute to the kinetic energy ? talk ) 22 : 48, 14 September 2012 ( UTC)
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The energy equation used for open channel flow computations is a simplification of the Bernoulli Equation ( See Bernoulli Principle ), which takes into account pressure head, elevation head, and velocity head . ( Note, energy and head are synonymous in Fluid Dynamics.
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A common misconception is that the head equals the fluid's energy per unit weight, while, in fact, the term with pressure does not represent any type of energy ( in the Bernoulli equation for an incompressible fluid this term represents work of pressure forces ).
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For more complicated situations the deflection can be determined by solving the Euler Bernoulli equation using techniques such as the " slope deflection method ", " moment distribution method ", " direct integration ", " Castigliano's method ", " Macaulay's method " or the " direct stiffness method ".
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The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure plus static pressure . " Total pressure " is also equal to dynamic pressure plus static pressure so, in incompressible flows, stagnation pressure is equal to total pressure . ( In compressible flows, stagnation pressure is also equal to total pressure providing the fluid entering the stagnation point is brought to rest isentropically .)
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