ChE 304
Uniform Acceleration Example
Tank Problem
An 80-cm-high fish tank of cross section 2m x 0.6m that is initially filled with water is to be transported on the back of
a truck. The truck accelerates from 0 to 90 km/h in 10 s. If it is desired that no water spills during acceleration,
determine the allowable initial water height in the tank.
! p
r
¶∂ p
= g-a
= 0;
¶∂ p
= - ray ;
¶∂ p
= - r Hg + az L
¶∂ x
¶∂ y
¶∂ z
Writing in terms of the total differential
dp = - ray dy - r Hg + az L dz
Picking two points 1 and 2
p2 - p1 = - ray Hy2 - y1 L - r Hg + az L Hz2 - z1 L
Picking points 1 and 2 on the free surface yields p1 = p2 and
- ay
Dz = z2 - z1 =
Hy2 - y1 L
g + az
From trig
- ay
z2 - z1
= tan q =
y2 - y1
g + az
z2 - z1
tan q =
y2 - y1
Hz2 -z1 L
Hy2 -y1 L
h = 0.8 m;
b = 2 m;
w = 0.6 m;
v0 = 0 km ê hr;
vf = 90 km ê hr;
1000 m
hr
Dv = Hvf - v0 L
;
km
3600 s
Dt = 10.0 s;
q
2
UniformAccelerationInATank.nb
ay =
Dv
Dt
2.5 m
s2
az = 0;
g = 9.81
tanq =
m
s2
ay
;
g + az
0.254842
From the original figure
Long side orientated along the line of acceleration
Dz = b ê 2 tanq 100
cm
m
25.4842 cm
Short side orientated along the line of acceleration
Dz = w ê 2 tanq 100
7.64526 cm
cm
m