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Fluid Mechanics - Flow Through a Venturi Tube

If an incompressible fluid moves through a venturi tube (a tube purposefully built to be narrow in the middle), the continuity principle tells us the fluid velocity must increase through the narrow portion. This increase in velocity causes kinetic energy to increase at that point. If the tube is level, there will be negligible difference in elevation (z) between different points of the tube’s centerline, which means elevation head remains constant. According to the Law of Energy Conservation, some other form of energy must decrease to account for the increase in kinetic energy. This other form is the pressure head, which decreases at the throat of the venturi:

 

 

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” represented1 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:

 

 

1The 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.


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Comments (2)Add Comment
0
Mr.
written by Andrew, August 30, 2014
If the pressure decreases in the throat, does temperature also decrease in the throat, and if so why?
0
Hi
written by BenjaminSunners, November 27, 2017
Wow, amazing article! I would love to use is as a part of my essay at best essay writing service uk reviews. Stay strong!

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