Newtonian liquid/flow

A Newtonian liquid flows in steady state in a cylindrical pipe. 

II. Viscous flow through a capillary and flow processes between rotating cylinders. We shall try to calculate the viscous behavior for non-Newtonian liquids flowing... 

It is also possible to calculate the flow path in a Couette apparatus for non-Newtonian liquids (flowing between rotating cylinders Fig. 31) (see page 56). If an inner cylinder rotates at an angular velocity co and a shear deformation takes place in the gap between the internal and external cylinder (R — i a) we observe a torque M ... 

In designing the accessories and choosing an injection and extrusion installation for low-pressure moulding1, it is important to evaluate the design procedure for determining the channel resistance to non-Newtonian liquid flow. Practically simple and convenient design procedures for pressure losses and hydraulic resistance of non-round channels for power liquids and liquids described by the three-parameter model may be found, e.g. in 68,69). 

When there is a difference of pressure between two points of a capillary tube, the fluid flows from the high pressure side to the low pressure side of the tube. Let us assume that a Newtonian liquid flows through a capillary tube of radius r and length AL (Fig. 13.5). Once steady-state conditions are reached, that is, the applied energy is totally dissipated into friction energy, a simple balance of energy gives... 

Chandra K.G., Kale D.D., Pressure drop for two-phase air - non-Newtonian liquid flow in static mixers, Chem. Eng. J. 59 (1995), p. 277-280... 

Consider a layer of a newtonian liquid flowing in steady flow at constant rate and thickness over a flat plate as shown in Fig. 5.18. The plate is inclined at an angle jS with the vertical. The breadth of the layer in the direction perpendicular to the plane of the figure is b, and the thickness of the layer in the direction perpendicular to the plate is 8. Isolate a control volume as shown in Fig. 5.18. The upper surface of the control volume is in contact with the atmosphere, the two ends are planes perpendicular to the plate at a distance L apart, and the lower surface is the plane parallel with the wall at a distance r from the upper surface of the layer. 

When a non-Newtonian liquid flows through a 7.5 mm diameter and 300 mm long straight tube at 0.25 m /h, the pressure drop is 1 kPa. 

For an incompressible, Newtonian liquid flow, which is common for most electrokinetic dispensing applications, the flow field is described by the continuity equation... 

For a Newtonian liquid flow, this assumption is justified if the microchannel has a hydraulic diameter larger than 1 pm. In fact, for liquids the typical mean free path X of molecules under ambient conditions is 0.1-1 nm. Since the fluid velocity tends to evidence a slip at the microchannel walls for Knudsen numbers, defined as Kn = XjD, larger than 0.001, the no-slip botmdary condition has to be abandoned only when the hydraulic diameter of the microchannel becomes less than 1 pm. 

The analysis of the behavior of single-phase Newtonian liquid flow through microchannels in laminar and turbulent regime evidenced that the conventional theory validated for large channels holds for hydraulic diameters down to 10 pm. Further investigations are required for... 

According to the Hagen-Poiseuille law, the volumetric rate of flow of a Newtonian liquid flowing through the pores with a diameter of d i under the transmembrane pressure of Ap,m is given by... 

Mishra and Gupta presented pressure drop data for Newtonian liquid flowing through helical coils of different dimensions [102]. The coils were made of thick-walled, flexible, and smooth polythene pressure tubing of uniform circular cross section. They observed that the pitch had a negligible effect on pressure drop if it was less than the diameter of the coil. They modified the Dean number to incorporate the effect of pitch as... 

NON-NEWTONIAN LIQUID FLOW THROUGH GLOBE AND GATE VALVES... 

Non-Newtonian Liquid Flow Through Globe and Gate Valves 489... 

Fig. 7.10. Variation of laminar velocity with laminar radius for a Newtonian liquid flowing in a capillary (eqn (7.14)).

Most models currently available for blood filtration are based on empirical models/ Bruil proposed a mathematical model for leucocyte filtration process and could explain the filtration law in the plain membrane filter. However, the effect of direct interception in blood filtration is not clearly understood, and the particle capture efficiency may be modelled based on an empirical model proposed by Khilar and Fogler"" for Newtonian liquid flow. With the consideration of the further particle capture due to the reduction of the pore sizes and the porosity of filter fabric by particle bridging, pore blockage, and pore closure, a modified Khilar—Fogler model of the particle capture efficiency by Gruesbeck and Collins" may be applied in blood filtration. 

The entry pressure drop Pe generated when a Newtonian liquid flows very slowly (i.e. in creeping flow where Re <1) from a large radius reservoir into a smaller tube is (approximately) given by... 

The entry pressure drop Pe when a Newtonian liquid flows quickly from a large reservoir into the tube is given approximately by [6]... 

More generally, a Newtonian viscous liquid may be defined as one in which the components of stress at a given point in the liquid, at a given time, are linear functions of the first spatial derivatives of the velocity components at the same point and at the same instant. The general equations for Newtonian liquid flow may then be obtained from the elastic equations of an isotropic solid by replacing the strain components with the rate of strain components, remembering that, in a liquid, there is a hydrostatic stress —p, where p is the pressure, superposed on the viscous stresses. Equations [2.10] and [2.26] then become ... 

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