In problems involving electric or magnetic fields we visualize the fields by
introducing field lines (often called lines of force), which have the
properties that (1) they are everywhere tangent to the field vectors, and
(2) the density of the field lines is proportional to the magnitude
(strength) of the field. We can use the same method to visualize the
velocity field 
by introducing streamlines , which have the following properties:
A streamtube is a tubular region of fluid
surrounded by streamlines. Since streamlines don't intersect, the same
streamlines pass through a streamtube at all points along its length. Let's
take two cross-sections of a streamtube, with cross-sectional areas 
and 
(see Fig. 2.4).
Figure 2.4: A streamtube in a fluid.
If these areas are made small enough then the fluid velocities across the
cross-sections will be constant; let's call the speeds 
and 
(the
directions of the velocities being perpendicular to the cross-sections). The
rate at which mass is entering the streamtube is 
; the rate
at which it is leaving is 
. If the mass inside the
streamtube is not changing with time, so that the fluid is either
incompressible or in steady-state, we have
If, in addition, the fluid is incompressible, then 
, and we
have
so that the fluid speed increases when the cross-sectional area of the streamtube decreases. If this seems counter-intuitive, the following analogy might help. You drive down a four lane highway, and due to construction one lane on your side has been closed. The traffic crawls toward the point where the lane has been closed, with cars haphazardly merging into your lane. You finally hit the single lane, and whiz through the construction area. The cross-sectional area has decreased, and your speed has increased.
