Numbers using calculators

Assume an inlet liquid volumetric flow rate of 0.01 mVs, find the fluid velocity and then Reynolds number using calculated velocity. Use the Moody diagram to... 

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied ... 

Set this threshold to a small positive constant (the default value is 10" ° Hartree). This threshold is used by HyperChem to ignore all two-electron repulsion integrals with an absolute value less than this value. This option controls the performance of the SCF iterations and the accuracy of the wave function and energies since it can decrease the number of calculated two-electron integrals. 

Now that we know something about EDTA s chemical properties, we are ready to evaluate its utility as a titrant for the analysis of metal ions. To do so we need to know the shape of a complexometric EDTA titration curve. In Section 9B we saw that an acid-base titration curve shows the change in pH following the addition of titrant. The analogous result for a titration with EDTA shows the change in pM, where M is the metal ion, as a function of the volume of EDTA. In this section we learn how to calculate the titration curve. We then show how to quickly sketch the titration curve using a minimum number of calculations. 

Sketching a Redox Titration Curve As we have done for acid-base and complexo-metric titrations, we now show how to quickly sketch a redox titration curve using a minimum number of calculations. 

Various methods, such as influence sampling, can be used to reduce the number of calculations needed (Ref. 161). 

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

The advantage of the use of dimensionless numbers in calculations such as these is that they may be applied independent of the physical size of the system being described. 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

It can be seen from the previous description that the design of both a cold-feed stabilizer and a stabilizer with reflux is a rather complex and involved procedure. Distillation computer simulations are available that can be used to optimize the design of any stabilizer if the properties of the feed stream and desired vapor pressure of the bottoms product are known. Cases should be run of both a cold-feed stabilizer and one with reflux before a selection is made. Because of the large number of calculations required, it is not advisable to use hand calculation techniques to design a distillation process. There is too much opportunity for computational eiToi. 

Use Avogadro s number to calculate the mass of an atom or molecule. 

Exponential (or ordinary) numbers are readily raised to powers using a calculator. To square a number, use the x2 key. For example,... 

Figure 23. Plot of the experimental contact (Volta) potential difference atmetal/solventinterfaces ( r=0)vs. the values calculated by Jaworski898 as a function of solvent donor (DN) and acceptor (AN) numbers using the equation = 0.007 AN - 0.011 DN - 0.485. (Reproduced from...

DC current was supplied through the development and test sections for direct heating. The outer temperature on the heated wall was measured by means of an infrared radiometer. Experiments were carried out in the range of Re = 10-450. The average Nusselt number was calculated using the average temperature of the inner tube wall and mean temperature of the fluid at the inlet and outlet of the tube. 

Use Calculate Student s t-values given p and df Student s t is used instead of the normal deviate z when the number of measurements that go into a mean is relatively small and the assumption of p and a being infinitely precise has to be replaced by the assumption of a normally distributed mean and a x -distributed s. ... 

Today, when a pesticide with no detectable residues is registered for use, a Tolerance or maximum residue limit (MRL) is established at the lowest concentration level at which the method was validated. However, for risk assessment purposes it would be wrong to use this number in calculating the risk posed to humans by exposure to the pesticide from the consumption of the food product. This would be assuming that the amount of the pesticide present in all food products treated with the pesticide and for which no detectable residues were found is just less than the lowest level of method validation (LLMV). The assumption is wrong, but there is no better way of performing a risk assessment calculation unless the limit of detection (LOD) and limit of quantification (LOQ) of the method were clearly defined in a uniformly acceptable manner. 

Numbers used in this cycle AG° for dissociation of monomethyl sulfate to give sulfur trioxide, estimated above AG° for ionization of monomethyl sulfate AG° for ionization of methanol, calculated from the pA of methanol, 15.54.139)... 

Using Numbers Use the mass and volume data to calculate the densities of water,... 

Using Numbers Using the three points, draw the best-fit straight line through the points. Find the slope of the line. What are the units for the slope The value of the slope should look like another value you have previously calculated. Which one is it ... 

Measuring and Using Numbers Using the values for the current in Helmholtz coils (/) from Data Table 2, the value for k from Data Table 1, and the equation B = kl, calculate the values for magnetic field strength (B) and enter them in Data Table 3. Then calculate the square of the field strength (B2) and enter the values in Data Table 3. 

Measuring and Using Numbers Using the values in Data Table 3 and the equation e/m = 2V (B2r2), calculate the e/m ratios needed to complete Data Table 3. 

Atomic number Property Best method used Calculated value Known value... 

Use numbers to calculate corrected pressures and the product of pressure and volume. 

Measuring and Using Numbers Using the pressure data from Data Table 1, calculate the pressure of the dry air when the levels of the water in the leveling bulb and tube are the same. Record your answer in Data Table 2. 

Measuring and Using Numbers Use the relationship PV = k to calculate the constant for each of the sets of data. Record your answers in Data Table 2. 

Measuring and Using Numbers Use the moles of acetic acid and the molar mass of acetic acid to calculate the mass of acetic acid in the vinegar sample. 

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