Equation pressure drop

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

The relative pressure drop, AP, expression is based on the Fanning pressure-drop equation ... 

As with dust cyclones, no reliable pressure-drop equations exist (see Sec. 17), although many have been published. A part of the problem is that there is no standard cyclone geometry. Calvert (R-12) experimentally obtained AP = 0.000513 J Q /hiWi) 2.8hiWi/dl), where AP is in cm of water Pg is the gas density, g/cm is the gas volumetric flow rate, cmVs hj and Wj are cyclone inlet height and width respectively, cm and is the gas outlet diameter, cm. This equation is in the same form as that proposed by Shepherd and Lapple [Ind. Eng. Chem, 31, 1246 (1940)] but gives only 37 percent as much pressure drop. 

Pressure drop in a venturi scrubber is controlled by throat velocity. While some venturis have fixed throats, marw are designed with variable louvers to change throat dimensions and control performance for changes in gas flow. Pressure-drop equations have been developed by Calvert (R-13, R-14, R-15), Boll [Ind Eng Chem Fundam, 12, 40 (1973)], and Hesketh [J. Air Pollut Control Assoc, 24, 939 (1974)]. Hollands and Goel [Ind Eng Chem Fundam, 14, 16 (1975)] have developed a generalized pressure-drop equation. 

Calvert (R-15) critiqued the many pressure-drop equations and suggested the following simplified equation as accurate to 10 percent ... 

In general, the sonic or critical velocity is attained for an outlet or downstream pressure equal to or less than one half the upstream or inlet absolute pressure condition of a system. The discharge through an orifice or nozzle is usually a limiting condition for the flow through the end of a pipe. The usual pressure drop equations do not hold at the sonic velocity, as in an orifice. Conditions or systems exhausting to atmosphere (or vacuum) from medium to high pressures should be examined for critical flow, otherwise the calculated pressure drop may be in error. 

Kc = constant for Bolles bubble cap pressure drop equation, Figure 8-114... 

Closed and Open Loss Coefficients for Dry Tray Pressure Drop Equations 8-314 and 8-315... 

Pressure drop equation For IMTP packing, non-foaming system, use Figure 9-21G or I. 

B = Rate of blowdown, (cooling tower), gpm or = constant in pressure drop equation for cooling tower... 

C = Constant in pressure drop equation for cooling towers... 

Solution of Equation (8.63) for the case of constant viscosity gives the parabolic velocity profile. Equation (8.1), and Poiseuille s equation for pressure drop. Equation (3.14). In the more general case of /r = /r(r), the velocity profile and pressure drop are determined numerically. 

Note the friction factor used in equation 5.3 is related to the shear stress at the pipe wall, R, by the equation / = (R/pu2). Other workers use different relationships. Their charts for friction factor will give values that are multiples of those given by Figure 5.7. So, it is important to make sure that the pressure drop equation used matches the friction factor chart. 

When a gas flows through a pipe the gas density is a function of the pressure and so is determined by the pressure drop. Equation 5.3 and Figure 5.7 can be used to estimate the pressure drop, but it may be necessary to divide the pipeline into short sections and sum the results. 

The pressure drop equations apply to liquids. They also apply to compressible fluids for non-critical flow and AP < 10% Pb... 

The blower calculations are similar to those for the pumps. The optimum velocity for air is around 75ft/sec and the pressure drop is about 0.2 psi per 100ft of piping. At this velocity the kinetic energy term in the pressure-drop equation cannot be ignored. The pressure drop can be approximated if a 14 in. duct is specified and Figure 8-7b is used. 

In the foregoing discussion on network elements, we have not accounted for the elevation difference between the two vertices adjoining the network element. This difference, although negligible in many applications, is important in the transportation of liquids as, for example, in water distribution networks. In these applications a term pg(zj — z,) should be added to the pressure drop equation. 

Using the above exponents and pressure drop equations, the total pipeline air pressure drop and selected pressures were predicted for each Pipeline I, II and III, starting from the end of pipeline or points along the pipeline. Some of the predictions are presented in Fig. 17, from which it can be seen that the agreement between predicted and experimental values is quite good. 

The reaction is A - B + H2. The reactor length corresponding to the reactor volume and diameter specified is 110 m. The fA(x) and P(x) profiles can be determined by simultaneously integrating the material-balance equation (15.2-4) and the pressure-drop equation (15.2-11) ... 

Equations 6.5, 6.7 and 6.12 all relate to the energy changes involved for a fluid in steady turbulent flow. The most appropriate equation is selected for each particular application equation 6.12 is a convenient form from which a basic flow rate-pressure drop equation will be derived. 

Friction due to fittings, valves and other disturbances of flow in pipe lines is accounted for by the concepts of either their equivalent lengths of pipe or multiples of the velocity head. Accordingly, the pressure drop equation assumes either of the forms... 

The solution of the problem requires 14 — 7 = 7 more relations to be established. These are any set of 7 friction equations that involve the pressures at all the nodes. The material balances and pressure drop equations for this example are tabulated. 

A Network of Pipelines in Series, Parallel, and Branches the Sketch, Material Balances, and Pressure Drop Equations 101... 

We now formulate six material-balance equations for the six reactions (1) to (6) of the equations (7.151) to (7.156), as well as an energy balance and a pressure-drop equation. 

We now formulate six mass-balance DEs for the six reactions inside the reactor, as well as the energy-balance and pressure-drop equations. 

Having now established the friction factor f for the general pressure drop equation, the dimensional analysis equation for pipe pressure drop can be derived. A simple equation is now derived from the earlier Bernoulli equation ... 

The ordinary differential equations describing a steady-state adiabatic PFR can be written with axial length z as the independent variable. Alternatively the weight of catalyst w can be used as the independent variable. There are three equations a component balance on the product C, an energy balance, and a pressure drop equation based on the Ergun equation. These equations describe how the molar flowrate of component C, temperature T, and the pressure P change down the length of the reactor. Under steady-state conditions, the temperature of the gas and the solid catalyst are equal. This may or may not be true dynamically ... 

The component balance and pressure drop equation do not change, but the energy balance contains a heat transfer term... 

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