Overall pressure drop calculated

The reverse of this procedure may be important in design situations that is, the entrance correction must be known as a function and included in the overall pressure drop calculations. In extruder dies and spinerettes for fiber spinning, L/R values rarely exceed 10, and the entrance loss may be the major contribution to the overall pressure drop. Carley provides examples of design calculations involving these concepts. 

It should be noted that Equations 13.9 and 13.10 apply to smooth pipes, whereas the pipes used for transmission of fluids usually have some surface roughness, which increases the friction factor. However, for short fluid transmission pipes, the overall pressure drop is usually dominated by the pressure drop in the pipe fittings (valves, bends, etc). Thus, for short transmission pipes, there is little point in calculating the straight pipe pressure drop accurately. If the transmission pipe is long (>100 m) and straight, then the Fanning friction factor can be correlated as7 ... 

Pipe entrance and exit pressure losses should also be calculated and added to obtain the overall pressure drop. The loss in pressure due to sudden expansion from a diameter dtl to a larger diameter dl2 is given by the equation... 

A comparison between the data measured for the overall pressure drop across the impinging stream contactor and the corresponding values calculated with Eq. (4.25) is illustrated in Fig. 4.6. Good agreement between the results measured and calculated can be observed clearly, suggesting that the total pressure drop model established is reasonable and feasible for application. In addition, it has the advantages of universal applicability and convenience in calculation. 

Figure 4.6 Comparison between measured data and results calculated with Eq. (4.25) for the overall pressure drop cross the IS contactor. u0, m-s n9.48 011-06 ol2.64 A14.22 xl5.60...

On-line measurements of cake thickness during filter-system operation have not been feasible in most systems. However, when the pressure drop across the filter system, the gas flow rate, and the particle concentration in the incoming gases are measured, these data can be used to calculate the mass of filter cake on each filter. The overall pressure drop can be modeled as ... 

For quantitative validation of simulation results, it is often necessary to compare predicted profiles (of velocity or other variable of interest) with experimental data X-Y plotting facilities are useful for this purpose. Most post-processors allow the user to import tabulated data for comparison with simulation results. Facilities to calculate the usual global quantities of interest to reactor engineers, such as overall pressure drop, dispersed phase volume fraction, heat or mass transfer rates and so on, are necessary to address reactor engineering concerns. Most codes allow use of user-defined routines to evaluate different quantities of interest, which may then be displayed using the standard tools discussed above. 

With reference to the problem statement, calculate the overall pressure drop, AP, across the unit based on vendor data ... 

The solids flow rate can be controlled by non-mechanical valves such as an L-valve with a long horizontal leg. The overall pressure drop across an L-valve is normally calculated as a linear sum of two terms accounting for the pressure drop through the elbow and the pressure drop caused by the gas-solid flow in the horizontal leg [140] ... 

Equation 3-71 can be modified for calculating the overall pressure drop of the two-phase flow for the total length of pipe plus fittings, L from Equation 3-5, based on the gas-phase pressure drop. 

Calculate the overall pressure drop between points 1 and 2 for a 6-inch (Schedule 40, ID=6.065 inch) line for kerosene. Liquid conditions are flow rate - 900 gpm, density at 60°F, p = 51 lb/ft and temperature, t = 321°F. Figure 3-8 shows an isometric layout of the pipeline with fittings. 

The computer program PROG35 calculates the flow regime and the pressure drops for liquid and vapor phases. From the two-phase flow modulus, the overall pressure drop for the 6-inch pipe is calculated. Table 3-12 gives the input data and computer output of the two-phase... 

CALCULATE THE OVERALL PRESSURE DROP FOR LAMINAR FLOW, psi. 

VAPOR PRESSURE DROP. The flow of vapor through the holes and the liquid on the plate requires a difference in pressure. The pressure drop across a single plate is usually 50 to 70 mm HjO, and the pressure drop over a 40-plate column is then about 2 to 3 m H2O. The pressure required is automatically developed by the reboiler, which generates vapor at a pressure sufficient to overcome the pressure drop in the column and condenser. The overall pressure drop is calculated to determine the pressure and temperature in the reboiler, and the pressure drop per plate must be checked to make sure the plate will operate properly, without weeping or flooding. 

It is noticeable that at low flow rates the agreement between all the calculated and measured data is excellent, but the simplified analytical solution deviates from the other results at Reynolds numbers of between 300 and 1,000. Above these values a comparison of the analytical and modified analytical data clearly demonstrates the increasing importance of even relatively minor changes of pipe geometry in affecting the overall pressure drop when pumping non-Newtonian suspensions. 

The pneumatic conveying system of the previous example consists on 50 m horizontal pipe, two 0.5 m radius bends, and 15 m vertical pipe. Calculate the overall pressure drop on the system if the initial air velocity is 10% over the saltation velocity. 

The value of ratio 14 is then calculated from the Molerus diagram (Figure 5-10). The values of Xand APJL are then calculated from Equations 5-59 and 5-60. This step may be repeated for each range of particle size and summed up with other particle sizes to get an overall pressure drop for solids. However for Non-Newtonian mixtures additional procedures are needed. 

The arithmetical average of the pressure gradient at the tower top and the pressure gradient at the tower bottom, rather than Equation 8-1, may be used to calculate the overall pressure drop. This method only slightly overstates the pressure drop as long as the pressure gradient at the top is less than 2.5 times the pressure gradient at the bottom. 

Let us now try to estimate the overall pressure drop in the commercial reactor cyclone. The discussion in the main text of this chapter and in Chap. 4 leads us to expect the Eu number to be the same for the two. In addition, we can calculate Eu on basis of the inlet velocity ... 

For advanced modeling purposes, the addition of minor loss, flow field switchback, and manifolding effects can be approached analytically. In practice, however, the actual pressure drop in an cell or stack is very difficult to predict with high precision due to the effects of entry length, local turbulence, additional minor losses from switchback, consumption, uptake and other effects. Additionally, in PEFCs and AFCs with a porous diffusion media, there can be unintentional convective flow under the channels, which reduces overall pressure drop, as discussed in Chapter 6. Therefore, a good starting point is to assume the frictional pressure drop dominates (which has been found to be true in certain PFFCs [32]) and calculate an expected loss from Fq. (5.76). For a particular fuel cell, the pressure drop can be correlated as a function of entrance velocity, since this is relatively easy experimental data to obtain. 

An important concern in FCC riser submodels is how to calculate the slip factor, ip, and the average voidage, s, of the riser. The slip factor is simply defined as the ratio between gas velocity and catalyst particle velocity. The slip factor plays an important part in determining the residence time of reactions, and thus, affects the overall conversion in the riser. Harriot describes a slip factor range of 1.2 to 4.0 for most FCC risers but also indicates that there is no reliable correlation available for prediction [44]. Previous authors have used a variety of approaches including constant shp factor [45], multiple slip factors [46] and correlations [47]. An alternative approach is to include additional momentum balance equations for the gas phase and catalyst phase [48]. This approach allows users to calculate velocity profiles for each phase and the overall pressure drop in the riser directly. 

For two-phase flow, heat gain/loss is also an important consideration, because this dictates the vapor/liquid fraction of the flow. Apart from changing the overall physical properties, this also changes the flow regime and will have a substantial impact in pressure drop calculation. The heat loss/ gain can be used for compressible fluids for better results however, it is of less importance for multiphase flow, unless the thermodynamic correlations are used to estimate the vapor/liquid fraction of the fluid. 

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