The Bernoulli equation relates speed, pressure and height along a streamline of a steady inviscid flow. For constant mass density in uniform gravity,where is constant along that streamline. Each term has units of energy per unit mass. In a barotropic compressible fluid, the pressure term is instead .
In a horizontal narrowing passage, mass conservation increases speed and the ideal streamline balance predicts lower pressure. Pressure taps connected to a manometer can test this prediction. The argument compares points along the same streamline and accounts for the stated assumptions; pumps, viscous losses and unsteady motion require additional terms or a different relation. Equal values of on different streamlines require extra structure, such as a connected irrotational flow with a conservative body force.
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