Pressure acceleration term

The same procedure may be applied in principle to design of forced-recirculation reboilers with shell-side vapor generation. Little is known about two-phase flow on the shell side, out a reasonable estimate of the fric tion pressure drop can be made from the data of Diehl and Unruh [Pet Refiner, 36(10), 147 (1957) 37(10), 124 (1958)]. No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms. Tnese may be roughly estimated by assuming homogeneous flow. 

Using a homogeneous model proposed by Owens (1961) for low void fractions (a < 0.30) and high mass flux, as is usually encountered in a water-cooled reactor, the momentum change (or acceleration) pressure gradient term is obtained from... 

The frictional pressure gradient is obtained by different correlations described in following sections. In a horizontal flow, (dp/dz)elev = 0, it is an ideal case to perform experiments excluding the term of elevation pressure drop. Because of nonhomogeneity of the slug flow, the acceleration pressure gradient term is different from that shown above it is given in Section 3.5.2.2. 

The presence of slip also means that the acceleration term in the general governing equation [Eq. (15-45)] cannot be evaluated in the same manner as the one for homogeneous flow conditions. When the acceleration term is expanded to account for the difference in phase velocities, the momentum equation, when solved for the total pressure gradient, becomes... 

Draft Tube Pressure Drop. The pressure drop across the draft tube, AP2 3, is usually similar to that across the downcomer, APj 4, in magnitude. Thus, for a practical design basis, the total pressure drop across the draft tube and across the downcomer can be assumed to be equal. In most operating conditions, the pressure drop at the bottom section of the draft tube has a steep pressure gradient due primarily to acceleration of the solid particles from essentially zero vertical velocity. The acceleration term is especially significant when the solid circulation rate is high or when the draft tube is short. 

For single-phase flow the momentum balance can be written to give the static pressure drop as the resultant of acceleration, hydrostatic, and wall-friction pressure-drop terms. 

If the pressure drop in a pipeline is reasonable and the linear gas velosity is well below the speed of sound, the acceleration term in the equation of notion is usually neglected, and the pressure to mass flow correlation is described by eqn (4). 

The reaction is pressure accelerated and the data are interpreted in terms of a rather tightly bonded cyclic transition state in which the new bond formation has proceeded farther than bond breaking. Alternative transition states where only the ether carbon-oxygen bond is ruptured are considered unlikely. These data are then consistent with the small variation in rate with changing solvent polarity. 

In the calculation of the velocity profile of a hydrodynamic, fully developed, laminar flow we will presume the flow to be incompressible and all properties to be constant. The velocity profile of a fully developed, tubular flow is only dependent on the radius r, wx = wx(r) and wy = 0. Therefore the acceleration term gdw /dt in the Navier-Stokes equation (3.59) disappears body forces are not present, so fc = 0. An equilibrium develops between the pressure and friction forces. Balancing the forces on an annular fluid element, Fig. 3.32, gives... 

Circulation models are based on the equations of motion of the geophysical fluid dynamics and on the thermodynamics of seawater. The model area is divided into finite size grid cells. The state of the ocean is described by the velocity, temperature, and salinity in each grid cell, and its time evolution can be computed from the three-dimensional model equations. To reduce the computational demands, the model ocean is usually incompressible and the vertical acceleration is neglected, the latter assumption is known as hydrostatic approximation. This removes sound waves in the ocean from the model solution. In the horizontal equations, the Boussinesq approximation is applied and small density changes are ignored except in the horizontal pressure gradient terms. This implies that such models conserve... 

For steady flows, examination of (7-2) shows that the Reynolds number determines the relative magnitudes of the acceleration terms on the left-hand side and the viscous and pressure-gradient terms on the right. In the case of unsteady flows, the relative magnitude of... 

If there is a contraction in the volume of the reactants as they achieve the transition state, then the volume of activation is negative, the slope of the linear least-squares analysis is positive, and an increase in pressure accelerates the rate of conversion of reactants to products not only due to pressure terms in the rate law but also due to an increase in the kinetic rate constant at higher pressures in the vicinity of the critical point. 

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