Bagnold number

Bagnold Number ( $\mathrm {Ba}$ ${\ displaystyle \ mathrm {Ba}}$ ${\ displaystyle \ mathrm {Ba}}$ ) Is the similarity criterion used in the hydrodynamics of suspensions , which determines the relationship between the interaction of suspended particles and viscous friction. It is determined in one of the following ways:

\mathrm {Ba} ={\frac {m}{2L\eta }}{\frac {dv}{dz}}

{\ displaystyle \ mathrm {Ba} = {\ frac {m} {2L \ eta}} {\ frac {dv} {dz}}}

{\ displaystyle \ mathrm {Ba} = {\ frac {m} {2L \ eta}} {\ frac {dv} {dz}}}

or

\mathrm {Ba} ={\frac {{\sqrt {\lambda }}\rho d^{2}}{\eta }}{\frac {dv}{dz}},

{\ displaystyle \ mathrm {Ba} = {\ frac {{\ sqrt {\ lambda}} \ rho d ^ {2}} {\ eta}} {\ frac {dv} {dz}},}

{\ displaystyle \ mathrm {Ba} = {\ frac {{\ sqrt {\ lambda}} \ rho d ^ {2}} {\ eta}} {\ frac {dv} {dz}},}

Where

${\frac {dv}{dz}}$ ${\ displaystyle {\ frac {dv} {dz}}}$ ${\ displaystyle {\ frac {dv} {dz}}}$ - shear rate gradient ;
$\eta$ ${\ displaystyle \ eta}$ $\ eta$ - dynamic fluid viscosity ;
$\rho$ ${\ displaystyle \ rho}$ $\ rho$ - particle density of the suspension;
$d$ ${\ displaystyle d}$ $d$ - particle diameter of the suspension
$L$ ${\ displaystyle L}$ $L$ - characteristic length;
$m$ ${\ displaystyle m}$ $m$ - mass of suspended particles;
$\lambda =\left({\sqrt[{3}]{\frac {C_{0}}{C}}}-1\right)^{-1}$ ${\ displaystyle \ lambda = \ left ({\ sqrt [{3}] {\ frac {C_ {0}} {C}}} - 1 \ right) ^ {- 1}}$ ${\ displaystyle \ lambda = \ left ({\ sqrt [{3}] {\ frac {C_ {0}} {C}}} - 1 \ right) ^ {- 1}}$ - coefficient of linear concentration;
$C$ ${\ displaystyle C}$ $C$ - particle concentration;
$C_{0}$ ${\ displaystyle C_ {0}}$ $C_ {0}$ - particle concentration at $\lambda \rightarrow \infty$ ${\ displaystyle \ lambda \ rightarrow \ infty}$ $\ lambda \ rightarrow \ infty$ .

The Bagnold number determines the nature of the fluid flow with particles suspended in it. At $\mathrm {Ba} <40$ ${\ displaystyle \ mathrm {Ba} <40}$ ${\ displaystyle \ mathrm {Ba} <40}$ suspended particles have almost no effect on the flow of liquid, and when $\mathrm {Ba} >450$ ${\ displaystyle \ mathrm {Ba}> 450}$ ${\ displaystyle \ mathrm {Ba}> 450}$ particle collisions begin to affect and the flow takes on a special character ^[1] .

Named after British engineer Ralph Alger Bagnold .

Notes

↑ http://arxiv.org/pdf/patt-sol/9706004 .

Literature

Kyoji Sassa , Hiroshi Fukuoka , Fawu Wang Progress in landslide science
Massimo Greco , Armando Carravetta , Renata Della Morte River flow 2004

Links

https://web.archive.org/web/20100625233724/http://caltechbook.library.caltech.edu/51/1/nomen.pdf

[1] ttp://arxiv.org/pdf/patt-sol/9706004 .

Bagnold number

Notes

Literature

Links

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