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In fluid dynamics, a fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must decrease in accord with the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is balanced by a drop in pressure.
By measuring the change in pressure, the flow rate can be determined, as in various flow measurement devices such as venturi meters, venturi nozzles and orifice plates.
Referring to the diagram to the right, using Bernoulli's equation in the special case of incompressible flows (such as the flow of water or other liquid, or low speed flow of gas), the theoretical pressure drop at the constriction is given by:
{\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)} p_{1}-p_{2}={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)
where {\displaystyle \scriptstyle \rho \,} \scriptstyle \rho \, is the density of the fluid, {\displaystyle \scriptstyle v_{1}} \scriptstyle v_{1} is the (slower) fluid velocity where the pipe is wider, {\displaystyle \scriptstyle v_{2}} \scriptstyle v_{2} is the (faster) fluid velocity where the pipe is narrower (as seen in the figure).