Re: [問題] 導公式~

[wtp1022 (老鼠吱吱叫~~~)]

確實是用力平衡就可以導了
中間參雜了一些小技巧

推導如下
（可能會看的有點辛苦，請見諒）

from drag force :
F(D)=C(D)*A*ρ*(v^2)/2.........(A)
where
F(D)=drag force
C(D)=drag coeff.
A=cross section area
ρg=gas density
v=vertical settling velocity

from free falling equation:
F(I)=(ρp-ρg)*g*V............(B)
where
F(I)=impelling force or frr falling force in the fluid medium
ρp=particle density
g=acceleration const.
V=particle vol.

We must postulate that the settling follow the free settling mode,
that is there is no force other than drag force and  impelling force
will participate in the settling process; or we can say that particles
will not interact with each other during the settling process.

 if the settling follow the free settling, than (A) will equal to (B)
∴(ρp-ρg)*g*V=C(D)*A*ρ*(V^2)/2............(C)

and V=(π/6)d^3 (d=particle diameter)
A=(π/4)d^2

insert A and V in to (C)
∴v={4g*d* [(ρp-ρg)/ρg] / [3*C(D)] }^0.5..........(D)

if Re<1 we can assume it as the laminar flow (for external flow field)

so, C(D)=24/Re=24μ/ρp*v*d.....Stoke's Law
insert this into (D)
∴v=g*(ρp-ρg)*d^2 /18*μ............(E)

and u=Q/H*W
where
u=horizontal velocity=Q/H*W
(H*W=cross section area of the settling tank)
Q=flow rate
H=settling tank height
W=settling tank width
∴Q = W*H*u.............(F)

and t=H/v(高度/沈降速)=L/u(長度/水平速)=Q/H*W*L(流率/槽體積)
where
t=overflow time or detention time
∴HWL/Q=H/v
v=Q/L*W............(G)

combine (G)and(F)
get v=H*u/L

finally we insert v into (E)

after equation operation
we can get

d=[18μ*u*H / g*L*(ρp-ρg)]^0.5
                                          #

Perhaps you can find out related equations in the
"particle operation text book" or the last few chapters in the
"McCabe & Smith Unit Operation"

※ 引述《o310177o (shain)》之銘言：
: 某一沉澱室中，其高度H、長度L，ρp、ρg分別為粒子與氣體的密度，μ為黏度，
: 要如何推導該室可沉澱的最小粒徑為下式
:                  ——————————
:  D(min)  =     ∕     18μHu
:               ∕——————————
:            ﹨∕    gL(ρp－ρg)
: 其中u指該粒子水平移動速度，另假設粒子之速度極慢，
: 即 Re< 0.1 (符合Stoke's law)
: 有人知道怎麼導嗎??
: 謝謝~~

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※ 編輯: wtp1022         來自: 114.33.236.221       (10/22 23:42)
※ 編輯: wtp1022         來自: 114.33.236.221       (10/22 23:43)
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