Radial pressure gradient

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

No radial pressure gradient over the cross section, i.e., ApL =... 

Consider an open bucket of water resting on a turntable that is rotating at an angular velocity on (see Fig. 4-5). The (inward) radial acceleration due to the rotation is o r, which results in a corresponding radial pressure gradient at all points in the fluid, in addition to the vertical pressure gradient due to gravity. Thus the pressure differential between any two points within the fluid separated by dr and dz is... 

The proper location of the heavy liquid weir (r2) can be determined by a balance of the radial pressure difference through the liquid layers, which is analogous to the gravity head balance in the gravity separator in Fig. 12-5. The radial pressure gradient due to centrifugal force is... 

Using the inviscid radial velocity profile yields an expression for the radial pressure gradient... 

The radial momentum equation is decoupled from the rest of the system, but can be used to determine the radial pressure gradient if needed. Again, substituting the scaled axial velocity and other definitions yields... 

Because the radial pressure gradient is expected to be generally negative in a protoplanetary disk, the result is that the gas will orbit the star slower than the solids (Adachi el al. 1976 Weidenschilling 1977a). Large solids, therefore, will feel a headwind as they attempt to follow Keplerian orbits. This drag force will... 

Chen, L., and Weinstein, H. The Radial Pressure Gradient in a Circulating Fluidized Bed Riser, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 187-192. Somerset, Pennsylvania (1993). 

Equation (3-66) is the balance between centrilugal forces and the radial pressure gradient that is responsible for the fact that ur = 0. Thus, in the Couette flow problem the acceleration associated with curved fluid pathlines does not necessarily lead to a radial flow, but may be balanced by a radial pressure gradient. 

However, the first of the terms on the right-hand side is the pressure gradient that is responsible for the radial flow. Clearly, this term cannot be smaller than terms on the left-hand side of (5-184), even for Re 1. The reason that it initially appears to be negligible is because we have scaled pressure with pc = (p.Vc/d)( /f2), which inappropriate for a flow that is dominated by viscous effects, but is not appropriate for Re 1. If we assume that we must retain the radial pressure gradient even for Re 1, this suggests... 

Because the radial pressure gradient in the core at leading order corresponds to ft = 1 we assume that the same is true in the boundary layer (essentially by matching). The boundary conditions for the function (/) are... 

Here, we have again assumed that the radial pressure gradient exactly matches that in the core at the same level of approximation. At the surface of the disk, F = (dF/dZ) = 0, and thus too... 

The variables in (12-114) including the coefficients C[ and C 2 are all dimensional, as indicated by the fact that they are primed. We see that the fluid moves in circular paths and thus the fluid particles undergo a centripetal acceleration. However, the centrifugal force associated with this centripetal acceleration does not produce a secondary flow, because it is exactly balanced by a radial pressure gradient,... 

As noted already in Chap. 3, the balance between centrifugal force and radial pressure gradient produces a potentially unstable arrangement that can be thought of as resulting from a gradient of angular momentum. 

Some recirculation is essential for flame stability. In many cases, the external recirculation originating from confined jets is insufficient to maintain a constant supply of hot gases and/or active species to maintain ignition. In this case, recirculation of hot gas must occur by some other means. The presence of swirl or of tangential velocity component results in the setup of radial and axial pressure gradients. The radial pressure gradient, given by... 

In addition to external current drive, the high-pressure fusion plasma itself can drive a so-called bootstrap current (Peeters 2000). This is generated by the radial pressure gradient, and therefore it is negligible in the center of the plasma and cannot be used for full current drive, but can substitute 50-70% of the total current in future high-pressure tokamak plasmas. 

Rotational flow in the forced vortex within the cyclone body gives rise to a radial pressure gradient. This pressure gradient, combined with the frictional pressure losses at the gas inlet and outlet and losses due to changes in flow direction, make up the total pressure drop. This pressure drop, measured between the inlet and the gas outlet, is usually proportional to the square of gas flow rate through the cyclone. A resistance coefficient, the Euler number Eu, relates the cyclone pressure drop Ap to a characteristic velocity v ... 

The free surface has the shape of a parabola (Figure 17.3), where the thickness of the fluid is smallest at the center. There is a radial pressure gradient which balances the centrifugal force, as shown by the Navier-Stokes equation [17.9a] for the radial component of the velocity. 

There is in the fluid a radial pressure gradient which balances the centrifugal force applied on a fluid particle. 

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