Flow Rate for Liquids

For the transition from Ligament to Film/Sheet Formation regime or the reverse transition, the equation of Hinze and MilbornJ112 QX = 0.340 Re2/3/We° 883, may be used to predict the dimensionless transition flow rate for liquids of low viscosities (less than a few poises). For more viscous liquids, the equation derived by Tanasawa et al.,[48°l QX = 0.297 Re6/5/We, is applicable for the calculation of the dimensionless transition flow rate. 

Dead time can result from measurement lag, analysis, and computation time, communication lag or the transport time required for a fluid to flow through a pipe. Figure 2.27 illustrates the response of a control loop to a step change, showing that the response started after a dead time (td) has passed and reaches a new steady state as a function of its time constant (t), defined in Figure 2.23. When material or energy is physically moved in a process plant, there is a dead time associated with that movement. This dead time equals the residence time of the fluid in the pipe. Note that the dead time is inversely proportional to the flow rate. For liquid flow in a pipe, the plug flow assumption is most accurate when the axial velocity profile is flat, a condition that occurs when Newtonian fluids are transported in turbulent flow. 

There are two types of capillary viscometers. In gravitational instruments, gravity drives vertical flow through a capillary and a timer is used to measure the flow rate. For liquids with low vapor pressures, an open-ended viscometer is suitable this design has been well studied, and commercial instruments are available. Accuracy of 1% or better can be achieved. For more volatile liquids,... 

The stationary discharge of gases or vapours from pipe leaks can be treated according to Example 10.3. Instead of the relationships for the velocity and mass flow rate for liquids the corresponding ones for gases of Sect. 7.4.3 have then to be used. 

Fig. 6. Oxygen pressurizing volume flow rates for liquid oxygen. Tank pressure, 300 psig tank volume, 0.312 ft average liquid flow.0.341 lb/secM /(>ly+4j >,0.804 U, 148.5 Btu/hr-ft - F theoretical curve from Equation (18).

Orifice Meter The most widely used flowmeter involves placing a fixed-area flow restriction (an orifice) in the pipe carrying the fliiid. This flow restriction causes a pressure drop that can be related to flow rate. The sharp-edge orifice is popular because of its simplicity, low cost, and the large amount of research data on its behavior. For the orifice meter, the flow rate for a liquid is given by... 

Convergence was achieved in 3 iterations. Converged values of temperatures, total flows, and component flow rates are tabulated in Table 13-14. Computed reboiler duty is 1,295,000 W (4,421,000 Btu/h). Computed temperature, total vapor flow, and component flow profiles, shown in Fig. 13-54, are not of the shapes that might be expected. Vapor and liquid flow rates for nC4 change dramatically from stage to stage. 

FIG. 13-109a Resp onses after a 30 percent increase in the feed flow rate for the mnlticomponent-dynamic-distillation example of Fig. 13-100. Profiles of liquid mole fractions at several times. 

Like thermal systems, it is eonvenient to eonsider fluid systems as being analogous to eleetrieal systems. There is one important differenee however, and this is that the relationship between pressure and flow-rate for a liquid under turbulent flow eondi-tions is nonlinear. In order to represent sueh systems using linear differential equations it beeomes neeessary to linearize the system equations. 

Back pressure reduces the pressure drop across the orifice of any type of PR valve. This results in reduced discharge rates in the case of vapors, if the back pressure exceeds the critical flow pressure. For liquids, any back pressure reduces the pressure drop and results in a lower discharge rate. 

Determine the values of the plate activation velocities (or load points), Fh, for the minimum as well as maximum liquid loads at top and bottom of the tower and any intermediate points exhibiting significant change in flow rates. For partial column area... 

Satisfactory operation must be between the upper and lower limits for both liquid and vapor flow rates. At liquid rates below 0.5 GPM per square foot of packing cross-section, liquid distribution is not uniform enough to ensure thorough wetting. At liquid rates between 25 GPM and 70 GPM per square foot of packing, the column is considered liquid-loaded and becomes very sensitive to additional liquid or vapor flow. 

Liquid face velocity rates (flow rates) for organic removal are usually less than 1 gpm/cu ft, but for chlorine are typically 2 to 3 gpm/cu ft. 

Cova (Cl 1) has examined the vertical distribution of catalyst concentration as a function of gas and liquid flow rates for systems with finite net liquid flow. A theoretical model is presented which predicts the catalyst profile as a function of physical properties and operating conditions, and which adequately represents observations for both laboratory and pilot-scale operations. 

Wall-to-bed heat-transfer coefficients were also measured by Viswanathan et al. (V6). The bed diameter was 2 in. and the media used were air, water, and quartz particles of 0.649- and 0.928-mm mean diameter. All experiments were carried out with constant bed height, whereas the amount of solid particles as well as the gas and liquid flow rates were varied. The results are presented in that paper as plots of heat-transfer coefficient versus the ratio between mass flow rate of gas and mass flow rate of liquid. The heat-transfer coefficient increased sharply to a maximum value, which was reached for relatively low gas-liquid ratios, and further increase of the ratio led to a reduction of the heat-transfer coefficient. It was also observed that the maximum value of the heat-transfer coefficient depends on the amount of solid particles in the column. Thus, for 0.928-mm particles, the maximum value of the heat-transfer coefficient obtained in experiments with 750-gm solids was approximately 40% higher than those obtained in experiments with 250- and 1250-gm solids. 

Figure 5 illustrates the experimental technique developed by Hewitt et al. for measuring the flow rate of liquid in the wall film as applied to flow inside a heated tube. As can be seen, a short length of porous sinter tube is positioned a few diameters beyond the outlet of the heated tube. The internal diameter of the sinter and the heated tube are made identical so as to avoid any flow... 

Micro-jet arrays are usually associated with lower energy consumption rates than sprays generated by the special (HAGO) nozzle for the same flow rate. The liquid was pushed through a 0.5 mm stainless steel orifice plate to form the jets. The holes in the plate were laser drilled and were arranged in a circular pattern giving a radial... 

In the preceding solvent extraction models, it was assumed that the phase flow rates L and G remained constant, which is consistent with a low degree of solute transfer relative to the total phase flow rate. For the case of gas absorption, normally the liquid flow is fairly constant and Lq is approximately equal to Li but often the gas flow can change quite substantially, such that Gq no longer equals Gj. For highly concentrated gas phase systems, it is therefore often preferable to define flow rates, L and G, on a solute-free mass basis and to express concentrations X and Y as mass ratio concentrations. This system of concentration units is used in the simulation example AMMONAB. 

For the open valve case (CONFLOl), make a step change in Pj and observe the transients in flow rate and liquid level. Try this for a sinusoidally varying inlet pressure. Experiment with a sudden change in the outlet valve setting. 

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