Piping conditions determination

The boundary conditions determine the form of balance equation for the inlet and outlet sections. These require special consideration as to whether diffusion fluxes can cross the boundaries in any particular physical situation. The physical situation of closed ends is considered here. This would be the case if a smaller pipe were used to transport the fluid in and out of the reactor, as shown in Figs. 4.13 and 4.14. 

Just as for isothermal flow, this is an implicit expression for the choke pressure (P ) as a function of the upstream pressure (Pi), the loss coefficients (J] Kf), and the isentropic exponent (7c), which is most easily solved by iteration. It is very important to realize that once the pressure at the end of the pipe falls to P and choked flow occurs, all of the conditions within the pipe (G = G, P2 = P, etc.) will remain the same regardless of how low the pressure outside the end of the pipe falls. The pressure drop within the pipe (which determines the flow rate) is always Pt — P when the flow is choked. 

The heat-transfer coefficient for the water flow on the inside of the pipe is determined from the flow conditions with properties evaluated at the bulk temperature. The free-convection heat-transfer coefficient on the outside of the pipe depends on the temperature difference between the surface and ambient air. This temperature difference depends on the overall energy balance. First, we evaluate /i,and then formulate an iterative procedure to determine h . 

Joza, P. and W.S. Rickert, and J. Kaiserman A comparison of yields of tar , nicotine and CO from pipe tobacco determined under various smoking conditions ... 

The diameters of pipe were determined by the throughput of effluent. The new landline is in two diameters, 1000 and 1200 mm, and collects effluent at manholes, into which the existing outfalls were diverted. The old outfalls to the river were retained as overflows from the manholes, to allow for excessive storm water conditions (Fig. 24.2). The sea outfall is 500 mm OD, narrowing at the diffuser end, 2.2 km out to sea, to extend the flow of effluent. 

The flow of traffic along a multilane highway can be described by the same mathematics that describes the flow of water in a system of pipes. The behavior of an electron bound to a single proton is described mathematically as a particle in a box, because it must conform to specific conditions determined by the confines of the box. The seemingly uniform movement of individual birds in flocks of flying birds demonstrates the chaos theory, in which discrete large-scale patterns arise from unique small-scale actions. This is also known as the butterfly effect. 

FIG. 5—Plot of metal loss versus exposure time for a carbon steel pipe, as determined by TLA. The depth of corrosion Is deduced from the activity loss of the test component The correct Inhibitor conditions were established between points a and c. At d, the component was removed for inspection and cieaned. After replacement, the apparent corrosion rate was very low, indicating the effectiveness of the inhibitor. 

The Poiseuille flow in a circular cylindrical pipe is determined in the same fashion as detailed above. The main difference is the need to represent the equations in a cylindrical coordinate system, since the boundary conditions are most optimum in that coordinate system. The equations are given in Table 1.2, and Figure 1.3 indicates the way in which a point M in space is located through the distance r to an axis Oa its abscissa z along that axis, and the angle 0. At that point, the flow velocity is determined by the components ur,ue, and Uz), represented on the basis of the three vectors er,ee, indicated in the figure. Therefore, the velocity vector is ... 

For calculation of the volumetric flow rate only the cross section area of the pipe is to be known. In order to give flow under standard conditions the temperature and pressure must be measured, and for conversion to mass flow the composition or density of the gas must be determined. These process parameters are often monitored by calibrated instrumentation. 

Once the mass flux G has been determined. Fig. 6-21r or Q>-2 h can be used to determine the pressure at any point along the pipe, simply by reducing 4fL/D and computing p From the Figures, given G, instead of the reverse. Charts for calculation between two points in a pipe with known flow and known pressure at either upstream or downstream locations have been presented by Loeb (Chem. Eng., 76[5], 179-184 [1969]) and for known downstream conditions By Powley (Can. J. Chem. Eng., 36, 241-245 [1958]). 

The specific resistance coefficient for the dust layer Ko was originally denned by Williams et al. [Heat. Piping Air Cond., 12, 259 (1940)], who proposed estimating values of the coefficient by use of the Kozeny-Carman equation [Carman, Trans. Inst. Chem. Fng. (London), 15, 150 (1937)]. In practice, K and Ko are measured directly in filtration experiments. The K and Ko values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental conditions. Values of Ko determined for certain dfists by Williams et al. (op. cit.) are presented in Table 17-5. 

The basis for design overpressure described in this section is related to the ASME Boiler and Pressure Vessel Codes and ANSI B31.3, Code for Petroleum Refinery Piping. Compliance with these codes is a requirement, or is recognized as the equivalent of a requirement in many locations. Where more stringent codes apply, the local requirements must be met. Therefore, local codes must be checked to determine their requirements. For example, some countries do not permit the use of block valves underneath pressure relief valves, unless dual valves with interlocks are installed. Also, in some cases, 20% accumulation under fire exposure conditions is not permitted, and accumulation allowed may be lower than the ASME Codes. In the United States, the ASME Code is mandatory, since it is a requirement under the Occupational Safety and Health... 

Two types of boundary conditions are considered, the closed vessel and the open vessel. The closed vessel (Figure 8-36) is one in which the inlet and outlet streams are completely mixed and dispersion occurs between the terminals. Piston flow prevails in both inlet and outlet piping. For this type of system, the analytic expression for the E-curve is not available. However, van der Laan [22] determined its mean and variance as... 

Normal operating pressure Anticipated process operating pressure used to determine pipe diameter requirements and pressure drop limitations for various operating conditions. 

Arrange the information from the previous steps and determine w Inch pipe size is best suited to all operating conditions. 

Usually either of these conditions requires a trial approach based upon assumed pipe sizes to meet the stated conditions. Some design problems may require determination of maximum flow for a fixed line size and length however, this just becomes the reverse of the conditions above. 

Note that determining the velocity at the inlet conditions to a pipe may create significant error when results are concerned with the outlet conditions, particularly if the pressure drop is high. Even the average of inlet and outlet conditions is not sufficiently accurate for some systems therefore conditions influenced by pressure drop can produce more accurate results w hen calculations are prepared for successive sections of the pipe system (long or high pressure). 

Figures 2-38A and 2-38B are based on the perfect gas laws and for sonic conditions at the outlet end of a pipe. For gases/vapors that deviate from these laws, such as steam, the same application will yield about 5% greater flow rate. For improved accuracy, use the charts in Figures 2-38A and 2-38B to determine the dowmstream pressure when sonic velocity occurs. Then use the fluid properties at this condition of pressure and temperature in ...

Determine the portion of a 30-mile, 18-in. (17.124-in. l.D.) line which must be paralleled with 20-in. (19.00-in. l.D.) pipe to raise the total system capacity 1.5 times the exisdng rate, keeping the system inlet and outlet conditions the same. 

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