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,

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