Buoyancy correction factor

Finally, if the object has a greater density than the weights (d0 > c/w), buoyancy correction factor will be less than 1.000000, because the smaller volume of the object displaces a smaller mass of air than the weights. Platinum, gold, and lead are metals with appreciably greater density than brass. 

The table which follows gives the values of k (buoyancy reduction factor), which is the correction necessary because of the buoyant effect of the air upon the object weighed the table is computed for air with the density of 0.0012 m is the weight in grams of the object when weighed in air weight of object reduced to in vacuo = m + m/1000. 

The resisting moment against overturning. The correction factor KOr is obtained as the ratio of lever arm r of the container weight Fgsc under buoyancy with and without deformation effect. 

It is instructive to compare the predictions of Eqs. (83) and (72) with the numerical solution obtained by Lloyd and Sparrow [24]. Table III shows that for large Prandtl numbers the difference is within 10%. The approximate equation is, unexpectedly, satisfactory even for low values of the Prandtl number if the buoyancy factor Bx is sufficiently small. Even though the error increases for larger values of Bx, this can be corrected by using the appropriate limiting values for Nux N and NuXiF. The first column in Table III for Pr = 0.72 is based on NuxN and Nux F for Pr - oo. The appropriate expressions for Prandtl numbers around unity are, however,... 

There is no point in using the very accurate density for water from Table 7-1 because the other densities are given only to two significant figures furthermore, the slight correction has almost no effect on the value of the factor or the true weight. If we used d0 = 0.9982 g/ml, the buoyancy factor would be 1.001052 and the true weight would be 99.9415 g. The error is only two parts in a million. 

Table 2-3 is provided to help with buoyancy calculations. Corrections for buoyancy with respect to stainless steel or brass mass (the density difference between the two is small enough to be neglected) and for the volume change of water and of glass containers have been incorporated into these data. Multiplication by the appropriate factor from Table 2-3 converts the mass of water at temperature T to (1) the corresponding volume at that temperature or (2) the volume at 20°C. 

Calibration of Mass. Calibration of mass is conducted by weighing a standard mass (over 1 /u,g) at a controlled temperature. Room temperature is preferable, since buoyancy and aerodynamics add to the uncertainty when the experiment is conducted over a wide range of temperatures. Any changes due to these factors go into a blank or background correction. 

Buoyancy effect This refers to apparent gain in weight that can occur when an empty and thermally inert crucible is heated. The effect is due to complex interaction between three factors (i) the decreased buoyancy of the atmosphere around the sample container at higher temperatures, (ii) the increased convection effect and (iii) the possible effect of heat from furnace on the balance itself In most modern thermobalances, attention to design factors has made the buoyancy effect negligible. However, if necessary a blank run with an empty crucible can be carried out over the appropriate temperature range. The resultant record can be used as a correction curve for subsequent experiments. 

The buoyancy, according to these differents factors, is especially significant at low temperature and will decrease at high temperature. When a mass variation has to be accurately measured at low temperature (for example water content), a correction of the buoyancy has to be performed. The common way is to run a blank test with an empty crucible with the same experimental conditions. However this numerical correction remains dependent on the reproducibility of such a blank curve and the correction is affected with a certain uncertainty. 

Factors (3), (5), (6), and (7) can be eliminated by good balance design, and (8) depends upon the operator. The main features influencing results are, therefore, (1), (2), and (4). Correction for change in buoyancy can be made from the curve for a thermally inert material. Factors (2) and (4) must be carefully assessed for each apparatus possible remedial modifications for one type of apparatus have been described by Lukaszewski [1962]. 

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