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,
1 A 1 v1t = 2 A 2 v2t
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,
A 1 v1 = A 2 v2
Hence the phrase "still water runs deep".
Click here for an Example.
(c) Doug Davis, 2001; all rights reserved
Fluid Flow Bernoulli's Equation Return to ToC, Fluids in Motion