Flow adiabatic

The starting point for development of the integrated adiabatic flow energy balance is Eq. (6.71) and again ideal gas behavior will be assumed. The equation of condition of a static adiabatic process, PV = const, is not applicable to the flow process the appropriate 

A limestone slurry of density 1.693 g/mL is pumped through a 4-in. (152 mm) line at the rate of 4 ft/sec (1.22 m/sec). The pressure drop (psi/mile) will be calculated. The slurry behavior is represented by 

Further substitutions from Eqs. (6.80) and (6.81) and multiplying through by IkgJG V result in 

When everything else is specified, Eqs. (6.86) or (6.88) may be solved for the exit specific volume Ej. Then Pj may be found from Eq. (6.81) or in the rearrangement 

In all compressible fluid pressure drop calculations it is usually justifiable to evaluate the friction factor at the inlet conditions and to assume it constant. The variation because of the effect of temperature change on the viscosity and hence on the Reynolds number, at the usual high Reynolds numbers, is rarely appreciable. 

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Adiabatic Flow with Friction in a Duct of Constant... 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

The equations for nozzle flow, Eqs. (6-114) through (6-118), remain valid for the nozzle section even in the presence of the discharge pipe. Equations (6-116) and (6-120), for the temperature variation, may also be used for the pipe, with Mo, po replacing Mi, pi since they are valid for adiabatic flow, with or without friction. 

The temperature obeys the adiabatic flow equation for a perfect gas. 

Equation (26-137) is recognized as the expression for aU-gas flow by adiabattc expansion across an orifice or nozzle. The factor k is the expansion coefficient for the adiabatic flow eqnahon of state ... 

To understand the flow in turbomachines, an understanding of the basic relationships of pressure, temperature, and type of flow must be acquired. Ideal flow in turbomachines exists when there is no transfer of heat between the gas and its surroundings, and the entropy of the gas remains unchanged. This type of flow is characterized as a rever.sible adiabatic flow. To describe this flow, the total and static conditions of pressure, temperature, and the concept of an ideal gas must be understood. 

The total enthalpy change across the whole (stationary) cooled blade row is straightforward and is obtained for the overall process (i.e. the complete adiabatic flow through control surfaces (A + B) plus (C)). Even though there is a heat transfer Q internally between the unit mainstream flow and the cooling air flow i//, from A to B, the overall process is adiabatic. 

Compressible fluid flow occurs between the two extremes of isothermal and adiabatic conditions. For adiabatic flow the temperature decreases (normally) for decreases in pressure, and the condition is represented by p V (k) = constant. Adiabatic flow is often assumed in short and well-insulated pipe, supporting the assumption that no heat is transferred to or from the pipe contents, except for the small heat generated by fricdon during flow. Isothermal pVa = constant temperature, and is the mechanism usually (not always) assumed for most process piping design. This is in reality close to actual conditions for many process and utility service applications. 

This paper surveys the field of methanation from fundamentals through commercial application. Thermodynamic data are used to predict the effects of temperature, pressure, number of equilibrium reaction stages, and feed composition on methane yield. Mechanisms and proposed kinetic equations are reviewed. These equations cannot prove any one mechanism however, they give insight on relative catalyst activity and rate-controlling steps. Derivation of kinetic equations from the temperature profile in an adiabatic flow system is illustrated. Various catalysts and their preparation are discussed. Nickel seems best nickel catalysts apparently have active sites with AF 3 kcal which accounts for observed poisoning by sulfur and steam. Carbon laydown is thermodynamically possible in a methanator, but it can be avoided kinetically by proper catalyst selection. Proposed commercial methanation systems are reviewed. 

In considering the flow in a pipe, the differential form of the general energy balance equation 2.54 are used, and the friction term 8F will be written in terms of the energy dissipated per unit mass of fluid for flow through a length d/ of pipe. In the first instance, isothermal flow of an ideal gas is considered and the flowrate is expressed as a function of upstream and downstream pressures. Non-isothermal and adiabatic flow are discussed later. 

The conditions existing during the adiabatic flow in a pipe may be calculated using the approximate expression Pi/ = a constant to give the relation between the pressure and the specific volume of the fluid. In general, however, the value of the index k may not be known for an irreversible adiabatic process. An alternative approach to the problem is therefore desirable.(2,3)... 

Integrating, a relation between P and v for adiabatic flow in a horizontal pipe is obtained ... 

Lawlb. C. . Trans. Am. Inst. Chem. Eng. 39 (1948) 385. Isothermal and adiabatic flow of compressible fluids. 

The plot of the pressure drop depending on the bulk velocity in adiabatic and diabatic flows is shown in Fig. 3.6a,b. The data related to the adiabatic flow correspond to constant temperature of the fluids Tjn = 25 °C, whereas in the diabatic flow the fluid temperature increased along micro-channel approximately from 40 to 60 °C. It is seen that in both cases the pressure drop for Habon G increases compared to clear water. The difference between pressure drop corresponding to flows of a surfactant solution and solvent increases with increasing bulk velocity. 

Fig. 3.6a,b Dependence of pressure drop on fluid bulk velocity in (a) adiabatic flow, and (b) diabatic flow. Reprinted from Hetsroni et al. (2004) with permission... 

CONTINUOUS CLOSED ADIABATIC FLOW TANK PROBLEM OF RAMIREZ... 

Pattern transition in horizontal adiabatic flow. An accurate analysis of pattern transitions on the basis of prevailing force(s) with flows in horizontal channels was performed and reported by Taitel and Dukler (1976b). In addition to the Froude and Weber numbers, other dimensionless groups used are... 

Pattern transition in vertical adiabatic flow. Upward vertical flow has been studied intensively, both because of the simplicity of the geometric condition and the relevance in applications. The map shown in Figure 3.4 is the result of rather recent and relevant studies into the interpretation of regime transition mechanisms. In this figure, the transition between bubbly flow and slug flow occurs be-... 

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