Valve equation

Yang W-C, Knowlton TM (1993) L-valve equations. Powder Technology 77 49-54... 

For a rotary valve, equation (9.20) is used to find the friction coefficient, C/j (jr), at a valve travel, x, ... 

The remarks made in Section 8.1 translate across to the gas flow cases more or less word for word, except that the methods of Chapter 9 must now be allied to those of Chapter 6 in order to calculate gas flow through line and valve. But the more complicated equations for both line flow and valve flow render explicit solutions to the full set of equations impossible. Two implicit methods, the Velocity-Head Implicit Method (VHIM) and the Smoothed Velocity-Head Implicit Method (SVHIM), will be presented, where the solution process has been reduced to iteration on a single variable. The SVHIM is judged to be more accurate because it deals with the compressible-flow valve equations at all times. 

SVHIM seeks to circumvent these problems by attacking the full set of line and valve equations at the outset. It is again necessary to solve the equations for subsonic and sonic flow in the valve separately, but the transition should now be smooth. The necessary equations for the subsonic case will now be listed in a logically consistent solution sequence. The basis of the method is first to guess and then to iterate on the value of the ratio of specific volumes Vi, /V2. 

The equations underlying ASVAM will now be set down for the plant arrangement of Figure 10.1. First we calculate the frictional loss in velocity heads in the same way as laid down for VHIM in Section 10.2 for the upstream section of pipe, the downstream section and the valve (equations (6.58), (7.36) and (7.25)), and then find the total frictional head loss, Kt, from equation (10.1). 

The ventricle model of Equation 8.12 was expanded to study closed-chest CPR [15]. The left ventricle was filled by a constant pressure source, and was coupled to the three-element modified windkessel arterial load, with mitral and aortic valves. Equation 8.12 includes a new term, pe (t), the external pressure applied directly to the ventricle during asystole and application of CPR ... 

The power loss from a process liquid stream going through a pressure letdown valve could be significant. If a power expander is considered to replace the letdown valve, equation (8.1) could be used to estimate the power recovery potential, and a typical power generation efficiency for a liquid expander is 75%. 

The constraint variable suggested in our previous study of fault-effect tree model (Lee et al., 1999) are used to increase the resolution. It represents the quantitative governing equation such as the balance equation and valve relation as variables. The previous study used a mass balance and two control valve equations for CSTR. As the control valve equations are expressed by DELS model, this study uses only mass balance equation. Reactor leaking (RX-LK) is a root cause of the positive deviation of the constraint variable, DF that is defined as Fq - Fp... 

Constant or Equal Percentage Valves. For an equal percentage valve, an equal change in the valve position causes an equal percentage change in flowrate. The valve equation for the constant percentage... 

It is further assumed that the correcting element has linear characteristics and that the control valve equation can be given by ... 

In Eq. 12-49 Amax min re the maximum and minimum allowable liquid levels, and hgp is the set point. Each is expressed as a percentage of the level transmitter range. In Eq. 12-47, V is the tank volume, and Qmax is the maximum flow rate through the control valve. Equations 12-47 and 12-49 ensure that the controller output will be at a saturation limit (0% or 100%) when the absolute value of the controller error is larger than Ah,... 

Modifled from McAvoy, 1983). A decanter shown in Fig. E18.14 is used to separate a feed that consists of two completely immiscible liquids, a light component and a heavy component. Because of the large difference in their densities, the two components form separate liquid phases very rapidly after the feed enters the decanter. The decanter is always full of liquid. The level of the interface I between the two liquid phases is measured by a dp cell. Each liquid flow rate can be adjusted by using a control valve, which is connected to a standard PI controller. The control valve equations relate flow rates, pressures, and controller output signals (mi, m2, m3) ... 

Determine the total holdup time Thu of the tank hy dividing the volume of the tank, as measured between the minimum and maximum level control points, by the maximum flow through the control valve (Equation 7.9). It is important to note that the volume in Equation 7.9 is the volume of the tank between minimum and maximum controlled levels, not the total tank volume. 

---