Newton number

Physical key figure
Surname	Newton number
Formula symbol	${\displaystyle {\mathit {Ne}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Ne}}={\frac {F_{\mathrm {W} }}{\rho v^{2}L^{2}}}}$
${\displaystyle F_{\mathrm {W} }}$ force ${\displaystyle \rho }$ density ${\displaystyle v}$ Flow velocity ${\displaystyle L}$ characteristic length
Named after	Isaac Newton
scope of application	Hydrodynamics

The Newton number is a dimensionless number that describes the ratio of the flow resistance force to the inertia force of the flow. It is named after the English physicist Isaac Newton and is defined as: ${\displaystyle {\mathit {Ne}}}$ ${\displaystyle F_{\mathrm {W} }}$

${\displaystyle {\mathit {Ne}}={\frac {F_{\mathrm {W} }}{\rho v^{2}L^{2}}}}$

is there

• ${\displaystyle \rho }$the density of the fluid
• ${\displaystyle v}$the flow velocity
• ${\displaystyle L}$a characteristic length

In viscous flows, such a flow resistance arises from eddies, for example . Referring to a flow caused by a difference in pressure comes about applies , so that the Newton number is identical to the Euler number ${\displaystyle \Delta p}$ ${\displaystyle F_{\mathrm {W} }=\Delta p\cdot L^{2}}$

${\displaystyle {\mathit {Eu}}={\frac {\Delta p}{\rho \,v^{2}}}}$.

If you consider a flow caused by gravity , the Newton number is the reciprocal of the Froude number . For internal friction, the Newton number is the reciprocal of the Reynolds number . ${\displaystyle {\mathit {Fr}}={\mathit {Eu}}^{-1}}$ ${\displaystyle {\mathit {Re}}={\mathit {Eu}}^{-1}}$

Application example

process technology

The Newton number is a dimensionless measure for, e.g. B. in a stirred tank , power introduced via a stirrer ; the definition is:

${\displaystyle {\mathit {Ne}}={\frac {P}{\rho n^{3}d_{R}^{5}}}}$ .

It indicates what proportion of the power of an agitator is actually available as hydraulic power . ${\displaystyle P}$ ${\displaystyle {\rho n^{3}d_{R}^{5}}}$

Formula symbol	designation	E.g. in SI units
${\displaystyle P}$	power	${\displaystyle \mathrm {W} }$
${\displaystyle \rho }$	density	${\displaystyle \mathrm {kg/m^{3}} }$
${\displaystyle n}$	rotational speed	${\displaystyle \mathrm {1/s} }$
${\displaystyle d_{R}}$	Stirrer diameter	${\displaystyle \mathrm {m} }$

Individual evidence

1. ^ ^{A b c} Josef Kunes: Dimensionless Physical Quantities in Science and Engineering . Elsevier, 2012, ISBN 0-12-391458-2 , pp. 75 ( limited preview in Google Book search).