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a statement of the conservation of energy in a form useful for solving problems involving fluids. for a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point

a special form of the euler’s equation derived along a fluid flow streamline is often called the bernoulli equation

for steady state incompressible flow the euler equation becomes (1). if we integrate (1) along the streamline it becomes (2). (2) can further be modified to (3) by dividing by gravity.

head of flow
equation (3) is often referred to the head because all elements has the unit of length.

dynamic pressure
(2) and (3) are two forms of the bernoulli equation for steady state incompressible flow. if we assume that the gravitational body force is negligible, (3) can be written as (4). both elements in the equation have the unit of pressure and it's common to refer the flow velocity component as the dynamic pressure of the fluid flow (5).

since energy is conserved along the streamline, (4) can be expressed as (6). using the equation we see that increasing the velocity of the flow will reduce the pressure, decreasing the velocity will increase the pressure.

this phenomena can be observed in a venturi meter where the pressure is reduced in the constriction area and regained after. it can also be observed in a pitot tube where the stagnation pressure is measured. the stagnation pressure is where the velocity component is zero.