HPP Activity 40v1
What is blood doing in our bodies?
Exploration
Up to this point we have been talking about static fluids, fluids that are not flowing. Now we are
going to study flowing fluids. This is called fluid dynamics.
We will do a gedanken (German for thought) experiment. Imagine going outside in the summer
to water the lawn. You attach a hose to the outside faucet.
GE 1.
1. Hold the end of the hose horizontally, turn the water on and observe the
water leaving the hose.
Use your finger to cover part of the opening at the end of the hose. Observe
the water leaving the hose. Can you make any statements about the velocity of
the water leaving the hose when it is partially covered with your finger
compared to the velocity of the water leaving the hose when the opening is not
covered by your finger based on your observations? Explain.
2. If you had two tubes of different radii attached to make one tube, as in the
diagram below, and water was flowing through the tubes, would the water
flow at the same velocity through the narrow part as through the wider part?
Explain.
Figure 1.
The amount of mass per unit time passing a cross-sectional area, A, of a pipe is called the flow
rate.
GE 2.
Consider a pipe that consists of two parts, one with a wider cross-sectional
area, as shown in the diagram below.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity 40v1
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Figure 2.
Consider the following statement, which refers to the above diagram:
If the liquid flowing does not build up in the pipe between area A1 and area
A2, then the mass per unit time passing cross-sectional area A1 must equal the
mass per unit time passing cross-sectional area A2.
1. Discuss this statement with your group members and see if they agree on
the meaning of this statement.
2.If this statement is true, would the velocity of the fluid be the same when it
crosses area A1 as when it crosses area A2? Or would the velocity of the fluid
as it crosses area A1 be greater or less than the velocity of the fluid as it
crosses area A2? Explain.
3.Is this consistent with your answer to questions in GE 1. ?
4. What factors do you expect the flow rate to depend on? List the factors.
Explain.
Invention
The flow rate can be written mathematically as
m/t
(1)
where m is the amount of mass crossing a cross-sectional area, A, in a time t. The flow rate
can also be defined mathematically as
m/t =  A1 v1
(2)
The flow rate, the mass per unit time passing a cross-sectional area A1, depends on the area, A1,
the velocity of the fluid in the pipe as it crosses area A1 (v1), and the density of the fluid.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 40v1
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If the flow rate is the same in each part of the pipe shown in the picture above, then
m/t =  A1 v1 =  A2 v2
(3)
and
A1 v1 = A2 v2
(4)
This is a mathematical statement of the continuity equation.
The continuity equation states that the velocity of a liquid flowing through a narrower part of a
pipe is greater than the velocity of liquid flowing through a wider part of a pipe.
Application
GE 3.
1. Show that the units are the same on each side of equation (2).
2. Let figure 2 be a model of a blood vessel that gets narrow, possibly due to
build-up of connective tissue and cholesterol deposits (arteriosclerosis).
Assume the flow is from right to left. If the cross-sectional area gets cut in
half, what happens to the velocity of the blood, assuming it behaves as an
ideal fluid?
Activity Guide
 2010 The Humanized Physics Project