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


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.

Fluid Flow

Bernoulli's Equation
Return to ToC, Fluids in Motion
(c) 2002, Doug Davis; all rights reserved