Graph paper

Experimental data often span many orders of magnitude. An example is the friction factor of a sphere moving through a fluid as a function of the Reynolds number, as discussed in Chapter 5. Some typical data for laminar flow are presented in Table D.l. 

Graph paper with a logarithmic scale on the ordinate and a linear scale on the abscissa is called semilog graph paper. An example of 2-cycle semilog paper is 

Correct No, we didn t use the proper coordinates to calculate the rise and run of the line. Equation (D.3) uses x and y. We need to use logio(x) and logiQ(y). Therefore 

To determine b (or actually, to determine 10 ), we substitute a point that lies on the line, such as x = 0.1, y = 100. This gives 

It is always prudent to check one s solution. Does the line go through another known point, such as x = 100, y = 10,000 Does 

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ASTM proposes representing the kinematic viscosity of hydrocarbons by a straight line on graph paper, called viscometric, for which the scales are such that ... 

Procedure. Using graph paper with Fig. 4-5 as a guide, construct the approximate carbon atom skeletons of cis- and rra./r.v-2-butene. 

Sketch the molecules on graph paper to help in determining the atomic coordinates. This is the first use of molecular geometry, a property that will become increasingly important as we go on. At this stage, the geometries are approximate the difference, for example, between cis and trans isomer s is ignored. 

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

This would give a straight line plot on rectangular graph paper. WeibuU graph paper plots [E(/), /] as a straight line. Figure 11 illustrates a typical WeibuU paper. 

In using WeibuU graph paper, a plotting position Pj = F tj) for theyth-ordered observation has to be decided. The mean or median are the principal contenders. The median can be conveniendy approximated (23) by... 

A straight line may be fitted to the (X, Y) or (X, Y) pairs of data when plotted on log-log graph paper from which the slope N and the intercept log K with X = 1 may be read. Alternatively, the method of least squares may be used to estimate the values of K and N, giving the best fit to the available data. 

There are a variety of ways to describe the droplet population. Figures 14-88 and 14-90 illustrate one of the most common methods, the plot of cumulative volume against droplet size on log-normal graph paper. This satisfies the restraint of not extrapolating to a negative drop size. Its other advantages are that it is easy to plot, the results are easy to visualize, and it yields a nearly straight line at lower drop sizes. 

If air quality data at a receptor for any one averaging time are lognormally distributed, these data will plot as a straight line on log probability graph paper (Fig. 4-9) which bears a note Sg = 2.35. Sg is the standard geometric deviation about the geometric mean (the geometric mean is the Nth root of the product of the n values of the individual measurements). 

Construet, on log-linear graph paper, using asymptotes, and validate using MATLAB or a similar tool, the Bode diagrams for... 

The Reactor Safety Study extensively used the lognormal distribution (equation 2.5-6) to represent the variability in failure rates. If plotted on logarithmic graph paper, the lopnormal distribution is normally distributed. 

Use of arithmetie graph paper tends to buneh at the lower end (due to the expansion of the sieve size seale). This ean be overeome by use of semi-log or log-log graph paper. Also note that eumulative graphs have the effeet of smoothing out the data. This ean be a useful effeet in the presentation of data Care should be exereised, however, to prevent important features of the distribution being obseured in analytieal work. 

Raste, /. notch, indentation detent, rasten, v.i. rest halt. — v.t. Radio) tune. Raster, m. screen grating graph paper. 

A nomograph is constructed by plotting dj/bj vs. Oj on log-log graph paper and then superimposing a YjD scale over the dj/bj scale, according to the values given in Table... 

Figure 14-21. Mollier diagram with expansion lines drawn for turbines with different numbers of stages. Note right vertical axis. Temperatures correspond to heavy Mollier lines and not the uniform graph paper lines. (Used by permission Althearn, F. H. Hydrocarbon Processing, p. 83, Aug. 1979. Gulf Publishing Co. All rights reserved.)...

The quantities K and m may also be found by plotting p vs. Q (flowrate) on log-log graph paper. Here, an outline of a hydraulic program design for the maximum jet impact force is presented. The jet impact force F. (lb) is calculated from... 

Unfortunately, these plots must be developed manually. The microprocessor-based systems generally do not automate this function, but they are easily constructed on graph paper. The following are the steps to construct such a plot ... 

The first step is to draw two horizontal lines on the graph paper. One is used to plot the vertical data and the other to plot the horizontal. These two lines show the location of each measurement point in inches with the outboard motor bearing being at zero. 

Determine the number of inches or mils that each block on the graph paper represents by first finding the distance from the back-foot of the stationary component to the back-foot of the movable component. Then determine the inches or mils per square that will spread the entire machine train across the graph paper. 

It must be noted, however, that a value of r close to either + 1 or — 1 does not necessarily confirm that there is a linear relationship between the variables. It is sound practice first to plot the calibration curve on graph paper and ascertain by visual inspection if the data points could be described by a straight line or whether they may fit a smooth curve. 

Plot the observed e.m.f. values against the concentrations of the standard solutions, using a semi-log graph paper which covers four cycles (i.e. spans four decades on the log scale) use the log axis for the concentrations, which should be in terms of fluoride ion concentration. A straight line plot (calibration curve) will be obtained. With increasing dilution of the solutions there tends to be a departure from the straight line with the electrode combination and measuring system referred to above, this becomes apparent when the fluoride ion concentration is reduced to ca 0.2 mg L-1. 

Saturated solutions of some reagents (T) 829 Schoniger oxygen flask see Oxygen flask Schwarzenbach classification 53 Screened indicators 268 Sebacic acid 469 Secondary pH standards 831 Selective ion meters 567 Selectivity coefficient, 559 in EDTA titrations, 312 in fluorimetry, 733 of analytical methods, 12 Selenium, D. of as element, (g) 465 Semi-log graph paper 572 Sensitivity (fl) 834, (fu) 732 Separation coefficient 163, 196 Separations by chromatographic methods, 13, 208. 233, 249... 

A graph paper based on this type of relationship can be obtained. It permits convenient graphical representation of size distribution data (as shown in Fig 3) even if the distribution does not follow a log-probability relationship. In addition, the assumption of a log-probability distribution as an approximation permits simple conversion from one basis of representing size distribution, mean size, or median size to another basis... 

The solid line typifies the shape of curve shown by actual materials on this type of plot. If a material obeys a log-probability relationship, the piot on this graph paper is a straight line, as... 

The notebook contains 114 pages of graph paper in a convenient 8 A X 11, 3-hole-punched format, carbon included. The new edition adds tables and graphs that make it a handy reference as well. 

Solution The classic way of fitting these data is to plot ln( /7 ) versus T" and to extract and Tact from the slope and intercept of the resulting (nearly) straight line. Special graph paper with a logarithmic j-axis and a l/T A-axis was made for this purpose. The currently preferred method is to use nonlinear regression to fit the data. The object is to find values for kQ and Tact that minimize the sum-of-squares ... 

Tn addition to the error due to the exposed stem, ordinary chemical thermometers of low cost are subject to errors due to irregularities in the bore and sometimes the scale graduations may not be very accurate. " It is therefore essential to check the thermometer at several temperatures against the melting points of pure solids or the boiling points of pure liquids as described below. The application of an exposed stem correction will of course be unnecessary if the thermometer is calibrated in this way. A calibration curve may then be drawn upon graph " paper from the data thus obtained. Temperatures at intervals of about 20° are marked as abscissae and the corrections to be added or subtracted as ordinates the points thus obtained are then connected by a smooth curve. The thermometer correction at any temperature may be read directly from the curve. 

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