Specification internal flow

There are two main reasons why a pump should not operate below its MCSF (/) the radial force (radial thmst) is increased as a pump operates at reduced flow (44,45). Depending on the specific speed of a pump, this radial force can be as much as 10 times greater near the shut off, as compared to that near the BEP and (2) the low flow operation results in increased turbulence and internal flow separation from impeller blades. As a result, highly unstable axial and radical fluctuating forces take place. 

Evans St Ablow (Ref 2) defined the steady-flow as "a flow in which all partial derivatives with.respect to time are equal to zero . The five equations listed in their, paper (p 131), together with. appropriate initial and boundary conditions, are sufficient to solve for the dependent variables q (material or particle velocity factor), P (pressure), p (density), e (specific internal energy) and s (specific entropy) in regions which.are free of discontinuities. When dissipative irreversible effects are present, appropriate additional terms are required in the equations... 

Heat duty (or internal How) specification. A composition or product rate specification may be substituted by a heat duty or internal flow (e.g., reflux) specification. This is done either to improve convergence in a computer simulation (especially if compositions are in the part per million levels), or in a revamp when the column or its exchangers are at a capacity limit. The mass, component, and energy balance equations translate this specification into a composition or product rate specification. Sections 4.2.3 and 4,3.1 have some further discussion. 

The option of specifying an internal flow instead of a purity specification is particularly useful with some of the methods described below that do not permit direct purity specifications. However, the larger number of options available to the user also increases the pitfalls of inconsistent specifications. These pitfalls are discussed in Secs. 4.3.1 and 4.8.2. 

Define the terms flow work, shaft work, specific internal energy, specific volume, and specific enthalpy. Write the energy balance for an open process system in terms of enthalpy and shaft work and state the conditions under which each of the five terms can be neglected. Given a description of an open process system, simplify the energy balance and solve it for whichever term is not specified in the process description. 

Explain the significance of the specific internal energies and enthalpies tabulated in the steam tables (B.5, B.6, and B.7), remembering that we can never know the true values of either variable in a given state. Given any process in which a specified mass (or mass flow rate) of water changes from one state to another, use the steam tables to calculate Af/ (or Af/) and/or (or H). 

A specific property is an intensive quantity obtained by dividing an extensive property (or its flow rate) by the total amount (or flow rate) of the process material. Thus, if the volume of a fluid is 200 cm and the mass of the fluid is 200 g, the specifle volume of the fluid is 1 cm /g, Similarly, if the mass flow rate of a stream is 100 kg/min and the volumetric flow rate is 150 L/min, the specific volume of the stream material is (150 L/min, 100 kg/min) = l.fLkgtii the rate at which kinetic energy is transported by this stream is 300 J/min. then the specific kinetic energy of the stream material is (300 J/rain)/ (100 kg/min) = 3 J/kg. We will me the symbol to denote aspecificproperty V will denote specific volume, U specific internal energy, and so on. 

The specific internal energy of helium at 300 K and 1 atm is 3800 J/mol, and the specific molar volume at the same temperature and pressure is 24.63 L/mol. Calculate the specific enthalpy of helium at this temperature and pressure, and the rate at which enthalpy is transported by a stream of helium at 300 K and 1 atm with a molar flow rate of 250 kmol/h. 

If more than one species is involved or if there are several input or output streams instead of just one of each, the procedure given in Section 8.1 should be followed choose reference states for each species, prepare and fill in a table of amounts and specific internal energies (closed system) or species flow rates and specific enthalpies (open system), and substitute the calculated values into the energy balance equation. The next example illustrates the procedure for a continuous heating process. 

In these equations n is the amount (mass or moles) of a species in one of its initial or final states in the process, h is the flow rate (mass or molar) of a species in a continuous stream entering or leaving the process, and 0 and H are respectively the specific internal energy and specific enthalpy of a species in a process state relative to a specified reference state for the same species. 

The Chilton-Colburn analogy has been obserx ed to hold quite well in laminar or turbulent flow over plane surfaces. But this is not always the case for internal flow and flow over irregular geometries, and in such cases specific relations developed should be used. When dealing with flow over blunt bodies, it is important to note that/in these relations is the skin friction coefficient, not the total drag coefficient, which also includes tlie pressure drag. 

For the operating parameters, it is necessary to specify five independent variables. A common method is to specify the four internal flow rates (Vi iv) and the switching time (SMB model) or solid flow (TMB model). Note that the four external flow rates have to fulfill the overall mass balance and supply only three independent specifications. 

To begin the calculations the column variables must be first initialized to some estimated values. Simple methods can be used for this purpose, based on the column specifications and possibly supplemented by shortcut methods. The column temperature profile may be assumed linear, interpolated between estimated condenser and reboiler temperatures. The values for Lj and Vj may be based on estimated reflux ratio and product rates, assisted by the assumption of constant internal flows within each column section. The compositions Xj- and T, may be assumed uniform throughout the column, set equal to the compositions of the liquid and vapor obtained by flashing the combined feeds at average column temperature and pressure. The other variables to be initialized are Rf,Rj, and Sj, which are calculated from their defining equations. The values for Qj may either be fixed at given values (zero on most stages) or estimated. 

L represents the tensor of the deformation velocities, q is the heat flow, r is the energy supply due to the external energy or heat sources, and e and are the specific internal energy and the specific internal energy production of the constituent y , respectively. 

The mass in this equation is expressed in kg, the flows in kg/s and the specific internal energy, the specific enthalpy in J/(kg K) and the specific volume in m /kg. We may convert to a kmol basis by dividing mass and mass flows by the average molecular weight, w, and by multiplying by w the specific internal energy, specific enthalpy and specific volume. Note that the energy input and power output (J) are unaffected ... 

Given an initial temperature for the node, T, it is possible to find the specific internal energy, u = u(T), and the specific volume, v = v(T), and hence the mass m = V/v. Equation (18.65), taken in conjunction with auxiliary equations (18.63), represents an implicit equation in the nodal pressure, p, which may be solved using the methods already outlined, either iteration or the Method of Referred Derivatives. The upstream and downstream flows, Wyp, and Wj , may then be found, so that it becomes possible to calculate the right-hand side of the temperature differential equation (18.64). Equation (18.64) may then be integrated to find the temperature of the node at the next timestep. The process may then be repeated for the duration of the transient under consideration. 

Fi is the flow of chemical species i (kmol/s), ill is the molar specific internal energy of species i (J/kmol),... 

We have now established a convenient way of specifying and representing the internal flow variables in the column. As mentioned previously, the designer is still required to specify an internal composition variable in the column. The choice of the compositional variable will be discussed in greater detail later, but for now it will suffice to state that we will specify the difference point of CS3 (X s). The reason behind choosing this specific variable and making an intelligent choice for it will become clear in the discussions in Section 7.3.3. 

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