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## Fluid Mechanics - Flow Through a Venturi Tube

Ideally, the pressure downstream of the narrow throat should be the same as the pressure upstream, assuming equal pipe diameters upstream and down. However, in practice the downstream pressure gauge will show slightly less pressure than the upstream gauge due to some inevitable energy loss as the fluid passed through the venturi. Some of this loss is due to fluid friction against the walls of the tube, and some is due to viscous losses within the fluid driven by turbulent fluid motion at the high-velocity throat passage.

The difference between upstream and downstream pressure is called permanent pressure loss, while the difference in pressure between the narrow throat and downstream is called pressure recovery.

If we install vertical sight-tubes called piezometers along a horizontal venturi tube, the differences in pressure will be shown by the heights of liquid columns within the tubes. Here, we assume an ideal (inviscid) liquid with no permanent pressure loss:

If we add three more piezometers to the venturi tube assembly, each one equipped with its own Pitot tube facing upstream to “catch” the velocity of the fluid, we see that total energy is indeed conserved at every point in the system. Here, each of the “heads” represented_{1} in Bernoulli’s equation are shown in relation to the different piezometer heights:

A more realistic scenario would show the influence of energy lost in the system due to friction. Here, the total energy is seen to decrease as a result of friction:

_{1}The form of Bernoulli’s equation with each term expressed in units of distance (e.g. z = [feet] ; = [feet] ; = [feet]) was chosen so that the piezometers’ liquid heights would directly correspond.

written by Andrew, August 30, 2014

written by BenjaminSunners, November 27, 2017

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