the volumetric flow versus pressure drop curve primarily linear, but there are other effects whichintroduce higher order terms. Most flow transducers suppliers are designed such that the outlet plenum has a smaller diameter than the inlet plenum. This eases the insertion and containment of the shunt between the sense inlet point and the sensor outlet point. If the shunt is removed, the energy of the gas must be conserved when passing from the inlet plenum to the outlet plenum. From Bernoulli’s 2 equation, so the sumof the kinetic energy and the pressure at each point must be a constant. Since all of the pressure drops are small, it can be assumed that the flow is incompressible. Typical Flow DividerThe pressure drop over the shunt can be shown to be: Fig 7.3Fig 7.3Fig 7.3Fig 7.3Fig 7.3
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We can see that even with no effect from the shunt there will be a pressure drop between thesensor inlet and outlet points. This pressure drop will be a strong function of the ratio of the two diameters. Since the drop is a square function of the flow velocity the differential pressure will be non-linear with respect to flow rate. Note also that the pressure drop is a function of density. The density will vary as a function of system pressure and it will also vary when the gas composition changes. This will cause the magnitude of the pressure drop due to the area change to be a function of system pressure and gas composition. Most of the shunts used contain or can be approximated by many short capillary tubes in parallel. From Rimberg1 we know that the equation for the pressure drop across a capillary tube contains terms that are proportional to the square of the volumetric flow rate. These terms come from the pressure drops associated with the sudden compression at the entrance and the sudden expansion at the exit of the capillary tube. The end effect terms are a function of density which will cause the quadratic term to vary with system pressure and gas composition. The absence of viscosity in the second term will cause a change in the relative magnitudes of the two terms whenever the viscosity of the flowing gas changes. PLQDQDKK 1288
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