Negative pressure gradient

Note In Volumes 1 and 2 this symbol is used for pressure difference, and pressure drop (negative pressure gradient) indicated by a minus sign. In this chapter, as the symbol is only used for pressure drop, the minus sign is omitted for convenience. 

The thickness indicated by the red line in Fig. 6.18 is the gap between the solid bed and the screw root. The screw root is moving in the minus z direction while the solid bed is moving in the positive z direction. Melted polymer will thus be dragged into the gap, and there will be a negative pressure gradient dP/dz in the film. This topic will be presented in Section 6.3.1.3. 

Particle velocity gradients near the wave-front are negative because the negative pressure gradient created by the overall reaction in the wave exceeds the expansion associated with local reaction... 

It can easily be verified that for regions > X for both positive and negative pressure gradients (i.e., both Cases a and b), Eq. E3.6-5 can be written as follows ... 

Note that Eq.6.4-8 indicates that for a positive pressure gradient (i.e., pressure rises in the positive x direction), v (0) < U, and for a negative pressure gradient, v (0) > U. 

Clearly, positive flow rate requires a negative pressure gradient, that is, a pressure drop or pressure loss. The pressure drop is given by... 

Q0 = 0, the fluid is simply carried down by the particles in their interstices at an equal velocity. It is possible to increase solids throughput by increasing fluid rates to yield values of Q0 < 0, thus producing a negative pressure gradient, as shown by the family of lines in the lower left quadrant of Fig. 12. 

The conventional sealing ability denotes the maximal negative pressure gradient with which the moving bed can be loaded. It is obvious that the theoretical sealing ability of a moving bed is equal to the bulk density of the solid particles, i.e.,... 

The ideal gas sealing condition is represented by line AOB for uj = 0, on which particles move while the fluid is at a standstill. When particles move downwards, the ideal sealing state uf = 0 can be realized under a negative pressure gradient, called the value of the ideal gas seal, which can be calculated... 

We can see from equation (5.13) that the largest velocity perturbations in the lower canopy will coincide with the position of the largest negative pressure gradient over the hill, which is well upwind of the hillcrest. 

The steady-state flow far from the input cross-section is characterized by a constant negative pressure gradient dP/dX = —AP/L = const (AP is the total pressure difference on the length L of the channel) moreover, the transverse velocity of the fluid is zero. The tangential velocity V = Vx depends only on the coordinate and satisfies the equation = -AP/L. By integrating this equation... 

Newtof)ian flow in a circular pipe We review the description of laminar flow in a circular pipe of radius R for a Newtonian fluid with constant viscosity p flowing under an imposed negative pressure gradient dP/dz= -t P/b,L. 

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