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(k> FALLING SPHERE V1 SCOMETER

The correction does not work with any degr of accuracy, and a number of empirical, BI theoreticaUy quite unsound expressions have bee proposed to modify it. As the Stokes’ eąuation ij its unmodified form only applies for very Iow speeds further terms may be added to allow for rather higher velocities. Ladenburg proposes an end Correction of the type

v(i-F mnst.d/Eji

if the sphere falls between twd rigid horizontal planes, h cm. apart. Various values have been proposed for the constant in this expression. In actual practice, the end correction can generally be neglected.

The falling sphere method is exceUent for many transparent materials, and can also be utilised for non-transparent materials by using metal spheres which indicate their presence through coils, Secording with valves. A very fuli account of this method is given in Barr’s book.

For relative measurements, Schofield suggests using two balls of different sizes in cylinders whose diameters bear an approximately constant. ratio to those of the balls. Scott Blair shows that this method works quite well for a true fluid, such as golden syrup. If a materiał is thixotropic, a con-dition (whidi will be discussed in Chapter VIII), in which the viscosity falls on stirring the Inaterial, and rises again on resting, then a measure of the thixotropy may be obtained from the ratio of the times of fali of the bali through a given distance, before and aftei stirring. Francis suggests the foUomng eąuation for the fali of a sphere in liouids of high viscosity m narrow tubes :_    ⁿ

11²S^RV | P) (i | R/^)»-«/9v

ib and Y are the radii of the vessel and of the _spS, and this equation is used in indastnai

^Al/the applications of Stokes' and of Poiseuille's ]_aws that have been dealt with so far depend on the hypothesis of streamline flow, *.<?., that the elements ofnow proceed in a straight linę parallel to the generał direction of flow. This was one of the three conditions postulated in deriving the generał eąuation relating velocity gradient to stress, and was not believed to be invalidated even in the case of materials showing the tr-phenomenon. It is not necessary for most practical rheologists to worry much about the comphcated physics of turbulent flow; but there are certain points which should be remembered. It is wise, if possible, to avoid turbulent conditions in flow measurements: if such conditions are inevitable, it should be noted that colloidal materials, as will be shown in the next chapter, do not obey the ordinaiy turbulence laws. The condition for turbulence for a true fluid, however, is fairly well understood. Reynolds' number (N) is defined as

2vRpJtj

where u is the velocity of flow, R is the radius of the tubę, p is the density and tj the viscosity. This may be written

where d is the diameter and K the kinematic viscosity. Turbulence normally occurs when N > 2,000, though in some cases much higher values have been reached before it sets in. Viscometers should be as smooth and regular as possible, as turbulence is frequently induced by irregularities