Bernoulli trinomial

The left-hand side of Eq. (2.1.3) is sometimes called Bernoulli s trinomial . The second term is unimportant relative to the two others when discussing gas cyclones and swirl tubes, since the fluid density is relatively low, and height differences not very large. 

In an actual flow situation, the fluid is not frictionless. Frictional dissipation of mechanical energy will therefore cause Bernoulli s trinomial to decrease in the flow direction, i.e. the trinomial is no longer constant, but decreases... 

Frictionless flow is, nevertheless, a reasonably good approximation in the outer part of the swirl in a cyclone, Bernoulli s trinomial does not change very much there. 

As the discussion in Sect. 2.1.1, and Eq. (2.A.12) show, in order for a rotating fluid element to maintain its equilibrium (static position in the r-direction), the pressure on its surface at higher r must exceed that on its surface a lower r. Thus the static pressure must increase monotonically with increasing radius. This, in fact, is borne out by experiment—a classic example of which is the data of Ter Linden (1953), a sample of which is presented in Fig. 3.1.2. Here the lower curves contained within each set of curves represents the variation in static pressure, p, with radial position the upper curves, the total pressure, p+(l/2)y0 (static plus dynamic). Comparing with Eq. (2.1.3) and realizing, as before, that the second term in Bernoulli s trinomial is small, we see from the profiles of total pressure in Fig. 3.1.2 that Bernoulli s trinomial is almost constant in the outer, nearly loss-free part of the vortex, while it decreases significantly in the center. This is as we would have expected. 

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See also in sourсe #XX -- [ , ]

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