Flujo Laminar Bingham
3
Modelo de Bingham τ xz =a−b ( dv z dx ) Método analítico PERFIL DE VELOCIDAD τ xz =a−b ( dv z dx ) a−( τ xz b )= dv z dx τ xz =ρg cos βx+ c 1 ¿ c 1 ¿ =0 dv z dx = a−( ρg cos βx b ) dv z = [ a−( ρg cos βx b ) ] dx ∫ dv z = ∫ [ a−( ρg cos βx b ) ] dx v z =ax− ( ρgcos βx 2 2 b ) + c 2 Si x=δ,v z =0 c 2 = ( ρg cos βδ 2 2 b ) −aδ v z =ax− ( ρg cos βx 2 2 b ) + ( ρg cos βδ 2 2 b ) −aδ v z =a ( x− δ) + ( ρg cos βδ 2 2 b ) ( 1− x 2 δ 2 )
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Transcript of Flujo Laminar Bingham
Modelo de Bingham
τ xz=a−b(dv zdx
)
Método analítico
PERFIL DE VELOCIDAD
τ xz=a−b(dv zdx
)
a−(τxzb
)=dvzdx
τ xz=ρg cos β x+c1¿
c1¿=0
dvzdx
=a−( ρgcos β xb
)
dv z=[a−( ρgcos β xb
)]dx∫ dvz=∫ [a−( ρg cos β x
b)]dx
vz=ax−( ρg cos β x22b )+c2 Si x=δ , vz=0
c2=( ρgcos βδ 22b )−aδvz=ax−( ρg cos β x22b )+( ρg cos βδ 22b )−aδvz=a ( x−δ )+( ρg cos β δ22b )(1− x2δ2 )
VELOCIDAD MÁXIMA
x=0
vz (max )=−aδ+( ρg cos β δ22b ) CAUDAL O FLUJO VOLUMETRICO
Q=∫0
δ
∫0
w
vz (x)dydx
Q=∫0
δ
∫0
w [a ( x−δ )+( ρg cos β δ2
2b )(1− x2δ2 )]dydxQ=∫
0
δ
w [a ( x−δ )+( ρg cos β δ2
2b )(1− x2δ 2 )]dx
Q=wa δ2
2−wa δ2+w ( ρgcos βδ 22b )(δ− δ 3
3δ 2 )Q=−wa δ
2
2+w ( ρgcos βδ 22b )( 23 δ)
VELOCIDAD MEDIA
⟨v z ⟩=∫0
δ
∫0
w
v z(x)dydx
∫0
δ
∫0
w
dxdy
⟨v z ⟩=−wa δ
2
2+w ( ρg cos βδ 22b )( 23 δ )
δw
⟨v z ⟩=−a δ2+( ρgcos βδ 22b )( 23 )
