Sampson flow

As Sampson flow , by Ralph Allen Sampson , the flow is in the English literature of a Newtonian fluid through a circular opening in a thin plate at low Reynolds numbers , respectively.

The strength of the volume flow is calculated according to:

{\ displaystyle {\ frac {\ mathrm {d} V} {\ mathrm {d} t}} = {\ frac {\ Delta pR ^ {3}} {3 \ eta}}}

It is

${\ displaystyle \ mathrm {d} V / \ mathrm {d} t}$ the volume flow through the opening,
${\ displaystyle \ Delta p}$ the pressure drop across the plate,
${\ displaystyle R}$ the radius of the opening and
${\ displaystyle \ eta}$ the dynamic viscosity of the fluid.

This relationship was published in 1891 by Sampson in his essay "On Stokes's Current Function" and in 1949 by R. Roscoe in his essay "The flow of viscous fluids round plane obstacles" was derived again and corrected for a calculation error.

The flow resistance of a flow through a cylinder of length is described by the Hagen-Poiseuille equation . This does not take into account the flow resistance due to the inflow and outflow at the cylinder ends. As a good approximation, this flow resistance due to the inflow and outflow in a straight cylinder can be taken into account by adding the flow resistance according to the equation given above to the flow resistance according to Hagen-Poiseuille. ${\ displaystyle L}$

{\ displaystyle {\ frac {\ mathrm {d} V} {\ mathrm {d} t}} = \ left ({\ frac {3} {R ^ {3}}} + {\ frac {8L} {\ pi R ^ {4}}} \ right) ^ {- 1} {\ frac {\ Delta p} {\ eta}}}

Individual evidence

^ RA Sampson: On Stokes's Current Function . In: Phil. Trans. Royal Soc. A . A, no. 182 , 1891, p. 449 , doi : 10.1098 / rsta.1891.0012 (the equation is in the appendix, page 514).
^ R. Roscoe: On the rheology of a suspension of viscoelastic spheres in a viscous liquid . In: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science . tape XXXI , no. 40: 302 , 1949, pp. 338–351 , doi : 10.1080 / 14786444908561255 (quotation Roscoe: "Sampson obtained an expression [...] differing by a factor of 4 on the righthand side as a result of trivial errors made in setting down his expressions for the stream function and totally flux. ").
^ HL Weissberg: An infinite-series solution for the creeping motion through an orifice of finite length . In: The Physics of Fluids . tape 5 , 1962, pp. 1033 , doi : 10.1063 / 1.1724469 .
↑ Z. Dagan, S. Weinbaum, R. Pfeffer: End Correction for Slow Viscous Flow through Long Tubes . In: Journal of Fluid Mechanics . tape 115 , 1982, pp. 505-523 , doi : 10.1017 / S0022112082000883 .

[1] RA Sampson: On Stokes's Current Function . In: Phil. Trans. Royal Soc. A . A, no. 182 , 1891, p. 449 , doi : 10.1098 / rsta.1891.0012 (the equation is in the appendix, page 514).

[2] R. Roscoe: On the rheology of a suspension of viscoelastic spheres in a viscous liquid . In: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science . tape XXXI , no. 40: 302 , 1949, pp. 338–351 , doi : 10.1080 / 14786444908561255 (quotation Roscoe: "Sampson obtained an expression [...] differing by a factor of 4 on the righthand side as a result of trivial errors made in setting down his expressions for the stream function and totally flux. ").

[3] HL Weissberg: An infinite-series solution for the creeping motion through an orifice of finite length . In: The Physics of Fluids . tape 5 , 1962, pp. 1033 , doi : 10.1063 / 1.1724469 .

[4] Z. Dagan, S. Weinbaum, R. Pfeffer: End Correction for Slow Viscous Flow through Long Tubes . In: Journal of Fluid Mechanics . tape 115 , 1982, pp. 505-523 , doi : 10.1017 / S0022112082000883 .