Washburn approach
4
z r θ The mold fill time and the average time the metal remains in the feed estimated using the laminar flow approach. See Gaskell section 2.6 fo laminar flow velocity profile inside a cylindrical pipe. The velocity inside the pipe because of the fluid:solid wall interaction gives a ~ pipe wall and the maximum fluid velocity is expected at the pipe cent the velocity profile at angle to the verticle is v z P L g cos R 2 r 2 4 The average velocity for a horizontal pipe is v Ave 1 R 2 0 2 0 R r v z r d d P L R 2 8 The volume flow rate is v vol 0 2 0 R r v z r d d P L R 4 8
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θ. z. r. Washburn approach. - PowerPoint PPT Presentation
Transcript of Washburn approach
z
r
θ
The mold fill time and the average time the metal remains in the feed tube can also beestimated using the laminar flow approach. See Gaskell section 2.6 for the derivation of thelaminar flow velocity profile inside a cylindrical pipe. The velocity of the fluid varies radially (r)inside the pipe because of the fluid:solid wall interaction gives a ~zero velocity at the insidepipe wall and the maximum fluid velocity is expected at the pipe center. For a pipe of radius R,the velocity profile at angle to the verticle is
vzPL
g cos
R2 r2 4
The average velocity for a horizontal pipe is
vAve1
R2 0
2
0
Rrvz r
d
dPL
R2
8
The volume flow rate is
vvol0
2
0
Rrvz r
d
d PL
R4
8
Washburn approach
vAve tL t( )( )d
d
PL
R2
8
P Pplunger Patm
Lo
LtLL t( )
dP
8 R2
0
t1
d
12Lo2
12Lt2
P
8 R2 t
12Lo2
12Lt2
P
8 R2 t
The solutions for L at time t are
1
2 4 Lo
2 P R2 t
1
2
1
2 4 Lo
2 P R2 t
1
2
t 0 .00001 0.25
L t R Lo 1
2 4 Lo
2 P R2 t s
1
2
0 0.02 0.04 0.060
2
4
6
L t 0.005 m 5 m( )
t
m
s
The average flow velocity for the plunger process is on the order of 5 m
6 10 2 s83.333
ms
.
This velocity is somewhat higher than that generally observed (55m/s). One problem is the assumption of laminar flow may not hold. Flow may be turbulent, which slows down the flow for a given pressure gradient
