Pressure acceleration losses

When a pure gas flows through a channel the accompanying fall in pressure is accounted for partly by acceleration of the flowing stream and partly by momentum transfer to the stationary walls. Since a porous medium may be regarded as an assembly of channels, similar considerations apply to flow through porous media, but in the diffusional situations of principal interest here accelerational pressure loss can usually be neglected. If more than one molecular species is present, we are also interested in the relative motions of the different species, so momentum transfers by collisions between different types of molecules are also important. 

Equation (14.128) can be used for calculating the pressure drop due to the acceleration of. solid particles provided that the velocity change C2 - C can be estimated. In addition to the acceleration pressure loss we have the normal" pre.ssure drop... 

The momentum pressure-drop can often be neglected, particularly when no mass transfer occurs in a system. Three equations, all approximate, are given below for calculation of these acceleration pressure losses, APa, between two sections, 1 and 2, using the mean velocities of gas and liquid,... 

It should be remembered that these correlations as originally devised by Lockhart and Martinelli were based almost entirely on experimental data obtained for situations in which accelerative effects were minor quantities. The Lockhart-Martinelli correlation thus implies the assumption that the static pressure-drop is equal to the frictional pressure-drop, and that these are equal in each phase. The Martinelli-Nelson approach supposes that the sum of the frictional and accelerational pressure-drops equals the static pressure-drop (hydrostatic head being allowed for) and that the static pressure-drop is the same in both phases. When acceleration pressure losses become important (e.g., as critical flow is approached), they are likely to be significantly different in the gas and liquid phases, and hence the frictional pressure losses will not be the same in each phase. In these circumstances, the correlation must begin to show deviations from experiment. 

In treating pressure losses in bends, Rose and Duckworth (1969) have suggested an empirical technique that considers only the acceleration portion of the pressure loss. Other analyses such as that of Yang may also be employed to calculate this acceleration pressure loss. 

In some installations, the incoming gas-solid mixture must be accelerated from a region of low velocity to that which exists at the entrance of the cyclone. Such a condition would exist at the inlet to a highly-loaded primary cyclone above a fiuidized bed, for example. If we apply the mechanical energy balance between a point located in the low velocity region (ahead of an inlet horn, for example) and a point in the high velocity region (within the horn) we obtain for the acceleration pressure loss. 

Pressure Drop. The pressure drop across a two-phase suspension is composed of various terms, such as static head, acceleration, and friction losses for both gas and soflds. For most dense fluid-bed appHcations, outside of entrance or exit regimes where the acceleration pressure drop is appreciable, the pressure drop simply results from the static head of soflds. Therefore, the weight of soflds ia the bed divided by the height of soflds gives the apparent density of the fluidized bed, ie... 

The flow resistance of pipe fittings (elbows, tees, etc) and valves is expressed in terms of either an equivalent length of straight pipe or velocity head loss (head loss = Kv /2g ). Most handbooks and manufacturers pubHcations dealing with fluid flow incorporate either tables of equivalent lengths for fittings and valves or K values for velocity head loss. Inasmuch as the velocity in the equipment is generally much lower than in the pipe, a pressure loss equal to at least one velocity head occurs when the fluid is accelerated to the pipe velocity. 

In ejectors and tube bends the most important part of the pressure loss comes from the acceleration of solid particles. In a bend the velocity of the particles is reduced due to the friction and the pressure loss is cairsed by the reacceleration of the particles after the bend. 

The pressure loss due to the acceleration of solids is obtained from Eq. (14.113) ... 

Divide the exchanger tube into sections and calculate the pressure drop section-by-section up the tube. Use suitable methods for the sections in which the flow is two-phase. Include the pressure loss due to the fluid acceleration as the vapour rate increases. For a horizontal reboiler, calculate the pressure drop in the shell, using a method suitable for two-phase flow. 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

A very good practice for avoiding pressure losses is the flared penetration, as shown in Figure 6.11. It is very common in LNG carriers and results in practically no pressure drop due to the smooth, non-turbulent acceleration of the product into the SRV inlet piping. 

Some of the structural factors, such as the changes in cross section area of flow passage and flow direction etc., may also cause pressure losses. Obviously, these factors depend on the specific structure of the device under consideration and vary from device to device. For convenience, and for more generalization, the resistance resulting from all the structural factors is represented in terms of the combined local resistance coefficient, 1s, which is also related to the velocity of the gas flow in the accelerating tube, i.e., the impinging velocity, utl. i.e.. 

On the resistance constitution of the equipment system, the major conclusions that can be drawn from the investigation are (1) Where millets or rapeseeds are the material to be processed, the power for the operation of the impinging stream contactor is mainly (>80%) consumed in the acceleration of particles (2) The pressure loss due to the impingement between the opposing streams is independent of the presence of solid particles. 

The acceleration length and the pressure loss in that length can also be estimated by using empirical correlations. Rose and Duckworth (1969) reported that... 

Two-phase flow pressure loss due to pipe-fitting acceleration... 

Please note that only the liquid-phase density p is used in Eq. (6.29). The reason that the average density is not used is that < > corrects for the gas-phase static leg AP. Equation (6.29) shows the second part of the three pressure losses occurring in two-phase flow. The final pressure loss calculation, acceleration, is covered next. 

Note that all the factors required for Eqs. (6.30) and (6.31) have been established in previous steps of this section. Thus, for any 90° standard ell using these two equations, we have the pressure loss established for two-phase flow acceleration. Simply multiply the calculated APen value by the number of 90° ells in the pipe segment. Remember that if a 15% pressure loss in a pipe segment results, a new pipe segment is required. 

The detection of pressure drop across a restriction is undoubtedly the most widely used method of industrial flow measurement. If the density is constant, the pressure drop can be interpreted as a reading of the flow. In larger pipes or ducts, the yearly energy operating cost of differential-pressure (d/p)-type flowmeters can exceed the purchase price of the meter. The permanent pressure loss through a flowmeter is usually expressed in units of velocity heads, v2/2 g, where v is the flowing velocity, and g is the gravitational acceleration (9.819 m/s2, or 32.215 ft/s2, at 60° latitude). 

In their second method, as in the case of a vertical riser, the total pressure drop along the spout height is composed of (i) a solids static head equivalent to the dispersed-solids bulk density, (ii) an acceleration pressure drop, and (iii) a solids friction loss due to relative motion of the particles with respect to the gas and to the spout wall. Thus,... 

The separator pressure losses are defined as the difference between the sums of static and dynamic pressure before and after the separator. To express the characteristic parameter corresponding to the pressure loss of a separator, the pressure loss coefficient is frequently used where the subscript D is related to the characteristic dimensions of the separator. The pressure loss coefficient depends on the pressure loss of the separator, gravitational acceleration, flow rate gas density and separator dimensions. 

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