Next: Pressure
Up: Fluids
Previous: States of Matter
Fluid Flow and the Continuity Equation
Fluids, by definition can flow, but are essentially incompressible.
This provides some very useful information about how fluids behave
when they flow through a pipe, or a hose. Consider a
hose whose diameter decreases along its
length, as shown in the Figure below. The ``continuity equation'' is a direct consequence of the
rather trivial fact that what goes into the hose must come out.
The volume of water flowing through the hose per unit time (i.e. the
flow rate at the left must be equal to the flow rate
at the right or in fact anywhere along the hose.
Moreover, the flow rate at and point
in the hose is equal to the area of the hose
at that point times the speed with which the fluid is moving:
You can easily verify that (area)x(velocity) has units m^{3}/t
which is correct for volume per unit time.
Figure 7.1:
Fluid flow in a hose of variable size

These considerations lead us directly to the continuity equation,
which states that
everywhere along the hose.
This has the important consequence that as the area of the
hose decreases, the velocity of the fluid must increase, in order to
keep the flow rate constant. Anyone who has pinched one end of a
garden hose has experienced this effect: the smaller you pinch the end
of the hose, the faster the water comes out.
Next: Pressure
Up: Fluids
Previous: States of Matter
modtech@theory.uwinnipeg.ca
19990929