Viscous pressure drop

Since x77 =f(z) for tapered dies, dx7,Jdz is nonzero. For reasonable taper values, they find these elastic forces to contribute less than 10% of the viscous pressure drop. They have also calculated the drag and pressure forces on the mandrel. 

The viscous pressure drop in the continuous (wetting) phase provides the force necessary to sustain motion of a ganglion in spite of the capillary forces. Darcy s Law for the wetting phase may be written as ... 

Viscous Pressure Drop. For continuous bubble trains with perfectly mobile interfaces moving through a given Dm channel, the dynamic pressure drop in the gas (foam) phase over a single tube segment D follows from Equation 16 ... 

Initial lymphatics in skeletal muscle have intraluminal valves that consist of bileaflets and a funnel structure [Mazzoni et al., 1987]. The leaflets are flexible structures and are opened and closed by a viscous pressure drop along the valve funnel. In closed position, these leaflets can support considerable pressures [Eisenhoffer et al., 1995 Ikomi et aL, 1997]. This arrangement preserves normal valve function even in initial lymphatics with irregularly shaped lumen cross sections. 

Using a simple scaling analysis, involving (1) viscous pressure drop, (2) hydrostatic pressure drop, (3) interfacial pressure drop and (4) penetration theory for mass transfer, it has been demonstrated that two-phase laminar bubble-train flow in small channels can exhibit better mass transfer for a given power input than turbulent contactors. 

Higgins, B.G., Scriven, L.E. Capillary pressure and viscous pressure drop set bounds on coating bead operability. Chem. Eng. Sci. 35, 673-682 (1980)... 

Apv stun of inertial and viscous pressure drops occurring in vapor phase... 

In order to do this, the viscous pressure drop APq of Fig. 6.66 is deducted from the total pressure drop APeo to give the electro or yield pressure APg for a particular voltage. Given the valve dimensions and using the dynamic viscosity as calculated from the zero-volts line and the valve dimensions, the yield stress at the wall may be isolated and 7 calculated. Likewise, shear stress T and y(= ujR/h) can be calculated from the shear mode test data -by neglecting radial effects. The well known relevant Poiseuille and Couette flow analysis are often used in these procedures. In both modes /r is derived from the zero-volts test. On this basis, flow- and shear- mode data will not necessarily correspond in the t, 7-plane. 

For the fluid polymer the inlet total pressure drop may be theoretically separated into viscous pressure drop,, and elastic pressure drop, [735]. 

For a LAD screen, the drag force is equal to the viscous pressure drop times the void fraction. Simplifying, Equation (3.28) becomes ... 

The term in parenthesis is the surface area to volume ratio a, and it is this relationship between a and r that makes the expression applicable to non-spherical packings. The constant C/2 is combined into a new constant a, and the viscous pressure drop term becomes ... 

Viscous and inertial frictional pressure losses and dynamic head pressure losses arise due to propellant flowing down the channel to the exit as indicated in the red arrows in Figure 3.13. Consider the vertically oriented LAD channel as shown in Figures 3.1 and 3.13, with the origin attached to the bottom center of the channel. The list of assumptions and corresponding implications used to solve for the viscous pressure drop inside the channel are as follows ... 

Equations (3.46) and (3.47) can then be used to solve for the viscous pressure drop in terms of the mass flow rate up the charmel ... 

Since the viscous pressure drop is linear with z ... 

Figure 6.9 Pressure required to form and eject an ink drop in inkjet printing. The acoustic pressure generated by an actuator must overcome the viscous pressure drop required to force liquid through the nozzle (frictional energy loss), the surface tension pressure rise to form the drop (surface energy), and the dynamic pressure (kinetic energy) of the liquid.

The acoustic pressure that is required to eject an ink droplet is shown schematically in Figure 6.9. To eject an ink drop, the acoustic pressure that is generated by the electrostatic actuator must overcome the viscous pressure drop required to push the ink through the nozzle ( 0.5-1 atm), the capillary pressure drop due to surface tension ( 0.1 atm), and the dynamic pressure of the liquid associated with its kinetic energy ( 0.5 atm). The total acoustic pressure required to eject a drop will be on the order of 1-2 atm of pressure. 

As the liquid returns from the condenser to the evaporator, it experiences a viscous pressure drop (APi), which can be written as... 

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