Entrance corrections

A capillary viscometer is a device in which the fluid under investigation is forced from a reservoir through a cylindrical capillary tube. They are operated with either flow rate or pressure as the independent variable. In the former case, the fluid is usually driven by a piston advancing through a cylindrical reservoir at a known constant rate with the force on the piston recorded in the latter case, regulated gas pressure drives the fluid and the volumetric flow rate is measured. 

Baglejr has developed a method for getting the true pressure gradient from capillaiy viscometer data. As seen in Fig. 16.4, 

The reverse of this procedure may be important in design situations that is, the entrance correction must be known as a function and included in the overall pressure drop calculations. In extruder dies and spinerettes for fiber spinning, L/R values rarely exceed 10, and the entrance loss may be the major contribution to the overall pressure drop. Carley provides examples of design calculations involving these concepts. 

Once the entrance correction has been established, it can be used to calculate the true equilibrium gradient through (16J15), which in turn is used in (16.5) and (16.21) or (16.22) to obtain the flow curve, relating the shear stress to shear rate, both at the tube wall In a few instances, other minor corrections have been applied, for example, considering the pressure drop in the viscometer reservoir.  

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Also worth noting in connection with the foregoing discussion is the experimental observation of a nonzero gauge pressure at the capillary exit PeK (Curve b of Fig. 12.5). Thus one must take into consideration end corrections, both entrance and exit, and not only entrance corrections alone, as was done by Bagley. Sakiades (6) was the first to report the existence of Pex for polymer solutions, and Han and his co-workers have studied it extensively using polymer melts (7-9). It has been found that Pex/APent is between 0.15 and 0.20, and that, although APent does not depend on L/Dq, Pex decreases up to L/Dq = 10, then remains constant (9). 

Te Nijenhuis K, "Viscoelastic Polymeric Fluids" Chap. 9.1 and "Entrance Correction and Extrudate Swell" Chap. 9.4 in Tropea C, Yarin AL and Foss JF (Eds) "Handbook of Experimental Fluid Mechanics", Springer, Berlin, 2007, Chap. 9.1. 

In these equations, is the shear stress at the capillary wall, AP. is the total pressure drop in the capillary, L is the capillary length, is an apparent length, and e is the Bagley entrance correction. 

Nonhomogeneous flow, only steady shear material functions Entrance corrections entail more data collection... 

Obtain dp/dx directly from pressure transducers no entrance corrections N by pex and especially pi, more rigorous than capillary die swell, but obtaining accurate N values is difficult Effect of finite slit width Cleaning slit comers... 

Figure 16.5 Bagley plot to determine entrance corrections.

SheUside flow maldistribution effect is normally iacluded in the, -correction. Tubeside flow maldistribution effect is relatively small in most designs because the principal resistances are tube friction and entrance/exit pressure drop. 

The temperature at the entrance to the impeller is increased because of the hot leakage. Calculate the corrected impeller inlet temperature using Equation 5.20. 

The problem of permeability exists whenever a plastic material is exposed to vapor, moisture, or liquids. Typical cases are electrical batteries, instruments, components installed underground, encapsulated electrical components, food packaging, and various fluid-material containers. In these cases, a plastic material is called upon to form a barrier either to minimize loss of vapor or fluid or to prevent the entrance of vapor or fluid into a product. From the designers viewpoint, the tolerable amount of permeation established by test under conditions of usage with a prototype product of correct shape and material is the only direct answer. 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

B3LYP predicts a negative overall barrier if X = Y = Cl (i.e. a barrier between the entry and exit ion-molecule complexes that lies below the entrance channel). Adamo and Barone [79] demonstrated that their new mPWlPW91 (modified Perdew-Wang) functional at least yields the correct sign for this problem. 

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