Family curves

At times you ll find that the information is the same, but the presentation of the curves is different. Almo-St all pump companies publish what are called the family of curves . The pump family curves are probably the most useful for the maintenance engineer and mechanic, the design engineer and purchasing agent. The family curves present the entire performance picture of a pump. 

On seeing and examining these different pump curves, notice that all curves contrast head and flow. And, in every ease the head is decreasing as the flow increases. 

Except for the curve of the PE) pump, the other pump curves show various diameter impellers that can be u.sed within the pump volute. And, on all the.se family curves, the effieieneies are. seen as eoneentrie ellipses. There is very little variation in the presentation of the BHp and 

Notice that the small drum pump doesn t show the NPSHr. This is because this pump, by design, can drain a bai rel or sump down to the bottom without causing problems. 

Up to this point, you probably didn t understand the crucial importance of the pump curve. With the information provided in this chapter, and this book, we suggest that you immediately locate and begin using your pump curves with suction and discharge gauges on your pumps. 

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The family curve shows the range of different impeller diameters that ean run inside the pump volute. They re normally presented as various parallel H-Q eurves eorresponding to smaller diameter impellers. 

Next, consider this family curve for a centrifugal pump used in the pulp and papermaking industry (Figure 7-13). 

The next graph is a typical family curve for a firewater pump (Figure 7-14) ... 

Observe this presentation of a family curve for a mag-drive pump used in the ehemieal proeess (Figure 7-15). 

Nowadays,. some pump companies publish their lamily curves on the Internet. You can request a copy with an e-mail, phone call, fax, or letter. The curves and gauges are the difference between life and death of your pumps. The pump family curve goes hand in hand with the system curve, which we ll cover in the next chapter. 

The purpose of the system eurve is to graphieally show the elements of the TDH imposed on the pump eurve. The systena curve shows the eomplete pieture of the dynamie system. This permits the purehase, installation, and naaintenanee of the best punap for the system. The system eurve is most useful when mated with the pump family eurve. This is why the family curves are the most useful to the design engineer, the maintenance engineer, and purehasing personnel. 

However, the concentration of impurity in the recycle is varied as shown in Fig. 8.5, so each component cost shows a family of curves when plotted against reactor conversion. Reactor cost (capital only) increases as before with increasing conversion (see Fig. 8.5a). Separation and recycle costs decrease as before (see Fig. 8.56). Figure 8.5c shows the cost of the heat exchanger network and utilities to again decrease with increasing conversion. In Fig. 8.5d, the purge... 

The family of curves consist of two straight-line portions, with a change of slope occurring at a degree of polymerization in the range 10 -10. ... 

Plot a family of curves, each of different n, with composition as the y axis and O2 absorbed as the x axis. Evaluate by Eq. (5.30) for n = 1, 2, 3, and 4 and 0.1 < p < 0.9 in increments of 0.1. Plot these results on y axis) on a separate graph drawn to the same scale as the experimental results. Compare your calculated curves with the experimental curves with respect to each of the following points (1) coordinates used, (2) general shape of curves, and (3) labeling of curves. 

The transition from laminar to turbulent flow occurs at Reynolds numbers varying from ca 2000 for n > 1 to ca 5000 for n = 0.2. In the laminar region the Fanning friction factor (Fig. 2) is identical to that for Newtonian fluids. In the turbulent region the friction factor drops significantly with decreasing values of producing a family of curves. 

Another member of the FGF family, FGF-4, protects against radiation-iaduced ceU killing and enhanced the G2 arrest when overexpressed ia a human adrenal cortical carcinoma ceU line (196). This effect is again manifested as the appearance of a shoulder on the survival curve, although neither the control nor the transfected cells undergo radiation-iaduced apoptosis. No differences ia the yield or repair of either SSBs or DSBs have been observed. 

Fig. 4. pM vs pH for A Cu(II), and B Mn (IT) EDTA chelates. For each family of curves, the lowest curve represents 1% the second, 10% and the top curve, 100% of free ligand species ia excess of the amount needed to form the metal chelate. Broken lines represent soHd—solution equiUbria for... 

Proportion of Hard Segments. As expected, the modulus of styrenic block copolymers increases with the proportion of the hard polystyrene segments. The tensile behavior of otherwise similar block copolymers with a wide range of polystyrene contents shows a family of stress—strain curves (4,7,8). As the styrene content is increased, the products change from very weak, soft, mbbedike materials to strong elastomers, then to leathery materials, and finally to hard glassy thermoplastics. The latter have been commercialized as clear, high impact polystyrenes under the trade name K-Resin (39) (Phillips Petroleum Co.). Other types of thermoplastic elastomers show similar behavior that is, as the ratio of the hard to soft phase is increased, the product in turn becomes harder. 

Comparison of Alignment Charts and Cartesian Graphs. There are typically fewer lines on an alignment chart as compared to Cartesian plots. This reduces error introduced by interpolation and inconsistency between scales. For example, to find a point (x,j) on a Cartesian graph one draws two lines, one perpendicular to each axis, and these reference lines intersect at the point x,j). This point (x,j) may correspond to some finite value found by rea ding a contour map represented by a family of curves corresponding to different values of the function. 

FIG. 22-55 Typical capital-cost schematic for membrane equipment showing trade-off for membrane area and mechanical equipment. Lines shown are from families for parallel hues showing hmiting costs for membrane and for ancillary equipment. Abscissa Relative membrane area installed in a typical membrane process. Minimum capital cost is at 1.0. Ordinate Relative cost. Line with positive slope is total membrane cost. Line with negative slope is total ancillary equipment cost. Curve is total capital cost. Minimum cost is at 1.0. 

Plots of E(L) and/(L) for various values of n appear in Fig. 23-9. The bell shapes of E t ) are more distinctive. The experimental curves of Figs. 23-10 and 23-11 clearly are of that family. 

Without recycle, washout occurs when D is greater than flmax, but recycle permits operation with D far greater than flmax- A family of curves is shown in Fig. 24-24 for concentrations of cell mass and nutrient at different recycle ratios. The distinct differences from Fig. 24-22 with no recycle are obvious. 

The family of short curves in Fig. 29-45 shows the power efficiency of conventional refrigeration systems. The curves for the latter are taken from the Engineering Data Book, Gas Processors Suppliers Association, Tulsa, Oklahoma. The data refer to the evaporator temperature as the point at which refrigeration is removed. If the refrigeration is used to cool a stream over a temperature interval, the efficiency is obviously somewhat less. The short curves in Fig. 29-45 are for several refrigeration-temperature intervals. A comparison of these curves with the expander curve shows that the refrigeration power requirement by expansion compares favorably with mechanical refrigeration below 360° R (—100° F). The expander efficiency is favored by lower temperature at which heat is to be removed. 

On the fig. 1 is given the family of curves displaying the dependence of chemi-luminescence intensity ver-sus time at injection of AO (the arrow shows the moment of inhibitor injection). 

The nomograph consists of a grid where two families of curves (for L and V) are placed and from two scales (vertical) for and II (in amperes xlO ). 

Figure 7 shows Eq for GaAs and Ga 82 0.18 function of temperature T to about 900 K. Additional measurements on samples having differing A1 contents would generate a family of curves. The solid line is a least-squares fit to a semi-empirical relation that describes the temperature variation of semiconductor energy gaps ... 

Note that the expression can be rearranged to obtain AP in terms of other variables. The expression can therefore be used to generate a family of curves of HP versus AP with GPM as a parametric variable. 

The magnitude of the variance a represents the square of the distribution spread and has the units of (time). The greater the value of this moment, the greater the spread of the RTD. The variance is particularly useful for matching experimental curves to one of a family of theoretical curves. 

Levenspiel [3] has given a family of Gaussian curves, and the equations representing these curves are given in Table 8-7. 

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