Equation of Continuity
V
= A l
l
= v t
m
= 
V
= A vt
Now, how can we handle this if the cross section A changes?
m1=
1 A 1
v1t
m2=
2 A 2
v2t
We are not creating nor destroying mass. The mass
m1
that flows into a region must equal the mass
m2
that flows out of the region. That is,
m1=
m2
1 A 1
v1t
= 2 A 2
v2t
or
1 A 1
v1 = 2
A 2 v2
For many situations -- for most situations involving a liquid but not a gas -- we can assume the density does not change. This is called an incompressible fluid. For those cases,
Hence the phrase "still water runs deep".
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