5.3 Fluid Flow Continuity
Physics Tool box
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Hydrodynamics – the study of fluids in motion.
Laminar Flow – the flow of the fluid is smooth, such that neighbouring
layers of the fluid slide by each other.
Turbulent Flow – is characterized by erratic, small whirlpool-like circles
called eddy currents.
Viscosity – internal frictions of the flowing fluid.
Equation of Continuity – The rate at which a fluid moves through a tube
with a single entry point and a single exit point remains the same, even if
the cross section of the tube varies.
A1v1  A2v2
The motion of a fluid can be extremely complex, as illustrated by currents in river
rapids, or the swirling smoke of a campfire. We can represent some situations by
relatively simple models.
An ideal fluid is a fluid that is incompressible (that is, its density cannot change) and
has no internal friction (viscosity). We define a flow line as the path of individual
particle in the moving fluid, and if the flow pattern does not change with time, the flow
is called steady flow. Flow lines that pass through the edge of an imaginary element of
area for a flow tube.
Laminar flow is flow in which the adjacent layers of fluid slide smoothly past each
other and the flow is steady.
In Turbulent flow there is no steady-state patterns, the flow pattern changes
continuously.
Continuity Equation
The mass of a moving fluid doesn’t change as it flows. This leads us to an important
quantitative relationship called the continuity equation.
In a flow tube with changing cross-sectional area, if the fluid is incompressible, the
product Av has the same value at all points along the tube.
A1v1  A2v2
Note: the continuity equation for compressible fluid is:
1 A1v1  2 A2v2
Example
Blood flows out of the heart into the aorta (inner radius of 0.009 m), where its speed is
m
. Eventually it reaches the capillaries in the body, where the fluid speed is
s
m
3.5 104 . Determine the cross-sectional area of the entire capillary system.
s
0.35
Solution:
Aaorta vaorta  Acap vcap
2
 raorta
vaorta  Acap vcap
Acap 
2
 raorta
vaorta
vcap
2
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  0.009m   0.35
3.5 104
 0.25m 2
m
s
m
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s