Número de Laplace

El número de Laplace (La), también conocido como Número de Suratman (Su), es un número adimensional utilizado en la caracterización de la mecánica de fluidos de superficies libres. Representa el cociente entre la tensión superficial y el transporte de momento (especialmente la disipación) dentro de un fluido.

Simbología

Simbología

Símbolo	Nombre	Unidad
${\displaystyle \mathrm {Ca} }$	Número de capilaridad
${\displaystyle \mathrm {La} }$	Número de Laplace
${\displaystyle \mathrm {Oh} }$	Número de Ohnesorge
${\displaystyle \mathrm {Re} }$	Número de Reynolds
${\displaystyle \mathrm {Su} }$	Número de Suratman
${\displaystyle \mathrm {We} }$	Número de Weber
${\displaystyle \rho }$	Densidad	kg / m^3
${\displaystyle \mu }$	Viscosidad	Pa s
${\displaystyle \sigma }$	Tensión superficial	N / m
${\displaystyle d}$	Dimensión de sección transversal	m
${\displaystyle L}$	Longitud	m

Descripción

Se define como:

${\displaystyle \mathrm {La} ={\frac {\text{Fuerzas de tensión superficial}}{\text{Fuerzas viscosas}}}}$

Deducción

	1	2
Ecuaciones	${\displaystyle \mathrm {La} ={\frac {\sigma \ (d^{2}/L)}{\nu \ (\nu \ \rho )}}}$	${\displaystyle \mu =\nu \ \rho }$
Multiplicando ${\displaystyle {\Bigl (}{\frac {\rho }{\rho }}{\Bigr )}}$	${\displaystyle \mathrm {La} ={\frac {\sigma \ (d^{2}/L)}{\nu \ (\nu \ \rho )}}{\Bigl (}{\frac {\rho }{\rho }}{\Bigr )}}$
Ordenando	${\displaystyle \mathrm {La} ={\frac {\sigma \ \rho \ (d^{2}/L)}{(\nu \ \rho )^{2}}}}$
Sustituyendo	${\displaystyle \mathrm {La} ={\frac {\sigma \ \rho \ (d^{2}/L)}{\mu ^{2}}}}$
Multiplicando ${\displaystyle {\Bigl (}{\frac {d\ L}{d\ L}}{\Bigr )}^{2}}$	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d\ L}{d\ L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ (d^{2}/L)}{\mu ^{2}}}{\Bigr )}}$
Simplificando	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}}$

${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}}$

Deducción

	1	2
Ecuaciones	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}}$	${\displaystyle \mathrm {Oh} ={\Bigl (}{\frac {L}{d}}{\Bigr )}{\frac {\mu }{\sqrt {\sigma \ \rho \ L}}}}$
Ordenando	${\displaystyle \mathrm {La} ={\frac {1}{[(L/d)\ \mu \ /{\sqrt {(\sigma \ \rho \ L)}}]^{2}}}}$
Sustituyendo	${\displaystyle \mathrm {La} ={\frac {1}{\mathrm {Oh} ^{2}}}}$

${\displaystyle \mathrm {La} ={\frac {1}{\mathrm {Oh} ^{2}}}}$

Deducción

	1	2	3
Ecuaciones	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}}$	${\displaystyle \mathrm {Re} ={\frac {\rho \ u\ d}{\mu }}}$	${\displaystyle \mathrm {Ca} ={\frac {\mu \ u}{\sigma }}}$
Multiplicando ${\displaystyle {\Bigl (}{\frac {u}{u}}{\Bigr )}}$	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}{\Bigl (}{\frac {u}{u}}{\Bigr )}}$
Ordenando	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}{\frac {(\rho \ u\ d)/\mu }{(\mu \ u)/\sigma }}}$
Sustituyendo	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}{\frac {\mathrm {Re} }{\mathrm {Ca} }}}$

${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}{\frac {\mathrm {Re} }{\mathrm {Ca} }}}$

Deducción

	1	2	3
Ecuaciones	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}}$	${\displaystyle \mathrm {Re} ={\frac {\rho \ u\ d}{\mu }}}$	${\displaystyle \mathrm {We} ={\frac {\rho \ u^{2}\ L}{\sigma }}}$
Multiplicando ${\displaystyle {\Bigl (}{\frac {\rho \ u^{2}}{\rho \ u^{2}}}{\Bigr )}}$	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {d}{L}}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma \ \rho \ L}{\mu ^{2}}}{\Bigr )}{\Bigl (}{\frac {\rho \ u^{2}}{\rho \ u^{2}}}{\Bigr )}}$
Simplificando	${\displaystyle \mathrm {La} ={\Bigl (}{\frac {\rho \ u\ d}{\mu }}{\Bigr )}^{2}{\Bigl (}{\frac {\sigma }{\rho \ u^{2}\ L}}{\Bigr )}}$
Sustituyendo	${\displaystyle \mathrm {La} ={\frac {\mathrm {Re} ^{2}}{\mathrm {We} }}}$

${\displaystyle \mathrm {La} ={\frac {\mathrm {Re} ^{2}}{\mathrm {We} }}}$

• Datos: Q179814