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. In choked
flow the mass flow rate will not increase with a further decrease in
the downstream pressure environment.
However, mass flow rate for a compressible fluid can 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.
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 (p1 − p2) at the constriction would be given by:
where is the density of the fluid, v1 is the (slower) fluid velocity where the pipe is wider, v2
is the (faster) fluid velocity where the pipe is narrower (as seen in
the figure). This assumes the flowing fluid (or other substance) is not
significantly compressible - even though pressure varies, the density
is assumed to remain approximately constant.
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