Operating points flow systems

The intersection of the characteristic curve (pump head) and the system head, illustrated in Figure 14, gives the operating point (flow rate) of the pump and pipe system. At this point the head generated by the pump is just balanced by the system head. 

Step 3. The final selection of a specific air blower and turboexpander must be made after fully considerating the results of Steps 1 and 2. The normal operating point must be located on the system operating map (similar to Figure 4-66) so that reasonable latitude is available in operating variables between normal operating point and air blower minimum flow, and between operating point and expander bypass point. 

Whether for a distillation, absorption, or stripping system the material balance should be established around the top, bottom, and feed sections of the column. Then, using these liquid and vapor rates at actual flowing conditions, determine the flooding and maximum operating points or conditions. Then, using Figures 9-21B, -21E, or -21F, establish pressure drop, or assume a pressure drop and back-calculate a vapor flow rate, and from this a column diam-... 

The static pressure difference will be independent of the fluid flow-rate. The dynamic loss will increase as the flow-rate is increased. It will be roughly proportional to the flow-rate squared, see equation 5.3. The system curve, or operating line, is a plot of the total pressure head versus the liquid flow-rate. The operating point of a centrifugal pump can be found by plotting the system curve on the pump s characteristic curve, see Example 5.3. 

When selecting a centrifugal pump for a given duty, it is important to match the pump characteristic with system curve. The operating point should be as close as is practical to the point of maximum pump efficiency, allowing for the range of flow-rate over which the pump may be required to operate. 

Most pump manufacturers provide composite curves, such as those shown in Fig. 8-3, that show the operating range of various pumps. For each pump that provides the required flow rate and head, the individual pump characteristics (such as those shown in Fig. 8-2 and Appendix H) are then consulted. The intersection of the system curve with the pump characteristic curve for a given impeller determines the pump operating point. The impeller diameter is selected that will produce the required head (or greater at the specified flow rate). This is repeated for all possible pump, impeller, and speed combinations to determine the combination that results in the highest efficiency (i.e., least power requirement). Note that if the operating point (Hp, Q) does not fall exactly on one of the (impeller) curves, then the... 

The point where the flow rate of 275 gpm intersects the system curve in Fig. 8-2 (at 219 ft of head) falls between impeller diameters of l and 7 in., as indicated by the O on the line. Thus, the P in. diameter would be too small, so we would need the 7 in. diameter impeller. However, if the pump with this impeller is installed in the system, the operating point would move to the point indicated by the X in Fig. 8-2. This corresponds to a head of almost 250 ft and a flow rate of about 290 gpm (i.e., the excess head provided by the larger impeller results in a higher flow rate than desired, all other things being equal). 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

A Throttling characteristics of centrifugal (c) -and positive- displacement (e, reciprocating d, rotary) pumps. B Control characteristics of positive displacement pumps a,b, Systems characteristics (b, after speed control) VFluid flow Ap, Differential pressure n, Speed h, Stroke length A, B, B, Operating points. 

Flow ratio control is essential in processes such as fuel-air mixing, blending, and reactor feed systems. In a two-stream process, for example, each stream will have its own controller, but the signal from the primary controller will go to a ratio control device which adjusts the set point of the other controller. Figure 3.17(a) is an example. Construction of the ratioing device may be an adjustable mechanical linkage or may be entirely pneumatic or electronic. In other two-stream operations, the flow rate of the secondary stream may be controlled by some property of the combined stream, temperature in the case of fuel-air systems or composition or some physical property indicative of the proportions of the two streams. 

The operating point may be found as the intersection of plots of the pump and system heads as functions of the flow rate. Or an equation may be fitted to the pump characteristic and then solved simultaneously with Eq. (7.16). Figure 7.17 has such plots, and Example 7.2 employs the algebraic method. 

Figure 7.17. Operating points of centrifugal pumps under a variety of conditions, (a) Operating points with a particular pump characteristic and system curves corresponding to various amounts of flow throttling with a control valve, (b) Operating point with two identical pumps in parallel each pump delivers one-half the flow and each has the same head, (c) Operating point with two identical pumps in series each pump delivers one-half the head and each has the same flow.

In order to simulate decreasing emission levels a truck engine of Euro III emission level (6 cylinder Volvo, displacement 7 liters) has been equipped with a continuously regeneration trap (CRT) filter system and an additional bypass to this filter by the Swiss EMPA institute. By a variation of the flow ratio of filtered/unfiltered exhaust gas, an emission level of about 60% of Euro IV has been adjusted (Mohr and Lehmann, 2003). The temporal courses of EC mass concentration and EC-specific surface area are depicted in Figure 34. In this graph, the mass and surface emissions of the 13 operation points within this test yield a different behavior. Most pronounced is the small specific surface area for idle operation which is caused by relatively large particles and in agreement to the results of previous studies. 

The screw extruder is equipped with a die, and the flow rate of the extruder as well as the pressure rise at a given screw speed are dependent on both, as shown in Fig. 6.16. The screw characteristic line at a given screw speed is a straight line (for isothermal Newtonian fluids). This line crosses the abscissa at open discharge (drag flow rate) value and the ordinate at closed discharge condition. The die characteristic is linearly proportional to the pressure drop across the die. The operating point, that is, the flow rate and pressure value at which the system will operate, is the cross-point between the two characteristic lines, when the pressure rise over the screw equals the pressure drop over the die. 

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