Poiseuille’s formula

In pneumatic nebulizers, the relative velocity of gas and liquid first induces a reduction in pressure above the surface of the liquid (see the calculation in Figure 19.4). The reduction in pressure is sufficient to cause liquids to flow out of capillary tubes, in accord with Poiseuille s formula (Figure 19.5). As the relative velocity of a liquid and a gas increases — particularly if the mass of liquid is small — this partial vacuum and rapid flow cause the surface of the liquid to be broken into droplets. An aerosol is formed. 

Using Poiseuille s formula, the calculation shows that for concentric-tube nebulizers, with dimension.s similar to those in use for ICP/MS, the reduced pressure arising from the relative linear velocity of gas and liquid causes the sample solution to be pulled from the end of the inner capillary tube. It can be estimated that the rate at which a sample passes through the inner capillary will be about 0.7 ml/min. For cross-flow nebulizers, the flows are similar once the gas and liquid stream intersection has been optimized. 

The actual correction found experimentally is k2V Qjn R rather than v Q l7fiR where k2 is a constant, nearly equal to unity, called the Hagenbach coefficient which depends on the form of the apparatus and must be determined by calibration in accurate, work. According to Boussinesqi its average value is M2. Poiseuille s formula (2) is thus modified to ( =1) ... 

Lutschinsky3 found that co increase with the atomic volume of the central atom R in chlorides RCI4 of the fourth group of elements, and (aM, where M is the molecular weight, is proportional to the linear dimension of the molecide. From Batschinsky s equation, and Poiseuille s formula for the effect of temperature, r]=r]ol(l+At+Bfi), Lutschinsky found ... 

We begin by simplifying Poiseuille s formula with the assumptions that pi = po, Pi = P2 + P where A p < pi, and A p2 < 2piAp so the second order term may be discarded,... 

The flow of liquids through capillary tubes was investigated experimentally by Wiedemann,2 O. E. Meyer, Graham, etc. the theory being developed by Stokes,5 Wiedemann, and Hagenbachthe latter obtained the formula (often called Poiseuille s law, which is really equation (1) above) ... 

Poiseuille s equation - A formula for the rate of flow of a viscous fluid through a tube ... 

Hagen-Poiseuille law, 72 Hagenbach coefficient, 74 correction, 73, 75 hanging drop, 183, 189 level viscometer, 80 Hare s apparatus, 12 Harkins s equation, 155 heat capacity of electrolyte solution, 225 content of electrolyte and non-electrolyte solutions, 225-6 content of vapour, 348 Heilborn s specific heat formula, 218 Henning s latent heat formula, 307 Herwig s method for density of saturated vapour, 325... 

Considering the Hagen-Poiseuille formula we find that the departures from the behavior expected from Newton s law can be represented, if we substitute for the Newtonian expression a more general relation between velocity gradient and shear stress. Many workers have endeavored to find an expression which would satisfy experimental facts. Rabino-witsch, Reiner and Weissenberg, particularly, have interested themselves recently in the anomalous behavior of viscous liquids. 

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