Editing Venturi effect (section)

==Background==
In [[inviscid flow|inviscid]] [[fluid dynamics]], an incompressible fluid's [[velocity]] must ''increase'' as it passes through a constriction in accord with the [[Continuity equation#Fluid dynamics|principle of mass continuity]], while its [[static pressure]] must ''decrease'' in accord with the principle of [[Mechanical energy#Conservation of mechanical energy|conservation of mechanical energy]] ([[Bernoulli's principle]]) or according to the [[Euler equations (fluid dynamics)|Euler equations]]. Thus, any gain in [[kinetic energy]] a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss in [[potential energy]].

By measuring the pressure difference without needing to measure the actual pressures at the two points, the flow rate can be determined, as in various [[flow measurement]] devices such as Venturi meters, Venturi nozzles and [[orifice plate]]s.

Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low-speed flow of gas) along a streamline, the theoretical [[static pressure]] drop at the constriction is given by

<math display="block">p_1 - p_2 = \frac{\rho}{2} (v_2^2 - v_1^2),</math>

where <math>\rho</math> is the [[density]] of the fluid, <math>v_1</math> is the (slower) fluid velocity where the pipe is wider, and <math>v_2</math> is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). The static pressure at each position is measured using a small tube either outside and ending at the wall or into the pipe with the small tube end face parallel with the flow direction. 

=== Choked flow ===
The limiting case of the Venturi effect is when a fluid reaches the state of [[choked flow]], where the [[fluid velocity]] approaches the local [[speed of sound]] of the fluid. When a fluid system is in a state of choked flow, a further decrease in the downstream pressure environment will not lead to an increase in velocity, unless the fluid is compressed.

The [[mass flow rate]] for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant).  This is the principle of operation of a [[de Laval nozzle]]. Increasing source temperature will also increase the local sonic velocity, thus allowing increased mass flow rate, but only if the nozzle area is also increased to compensate for the resulting decrease in density.

===Expansion of the section===

The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is a shortened expansion in the tube section, turbulence is more likely to appear, and the theorem will not hold. Generally in Venturi tubes, the pressure in the entrance is compared to the pressure in the middle section and the output section is never compared with them.