PRESSURE AND Fluid FLOW:
Pascal and Bernoulli
UM Physics Demo Lab 07/2013
Pre-Lab Question
A stream of water flows down a hill. Assuming no losses through friction, how does the
gravitational potential energy of one kilogram of water at the top of the hill compare with
the kinetic energy of the same kilogram of water when it reaches the bottom of the hill?
EXPLORATION
Materials
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Bernoulli Tank/Tub
aluminum ruler for tub
Large Plastic Tub – about 20” x 15” x 6”
plastic storage box ramp support (to aid in draining tub)
nylon plug (tank valve)
Homer bucket (to drain tub)
6’ Tygon Siphon tube
2’ Tygon tube
squeeze bulb
soda straw
veterinary syringe
plastic drinking cup
hair dryer
table tennis ball
plastic coke bottle
eye-dropper
½” cut steel washer
clear plastic ruler
calculator
sponge
Shared Components:
4 power strips
2 sponge mops
scrap paper
rags
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Atmospheric Pressure
Lab Tip: Many of these experiments require you to seal the end of a tube or
apparatus with your finger. For best results, always wet your finger when
using it to seal your experiment. The end of a plastic tube can also be sealed
by folding the end over and pinching it tightly.
1. Force some air out of your squeeze bulb and seal the end with your finger.
How does the pressure inside the bulb compare with the pressure in the room?
2.
What causes the squeeze bulb to remain compressed even after you are no
longer squeezing it with your hand?
3. Now draw some water up into the squeeze bulb. What produces the force on
the water necessary to make it move up into the bulb against gravity?
Empty the water from your squeeze bulb and attach it to the short plastic
tube. Holding the tube vertically, draw water up into the tube until the
bulb begins to fill. Fold the end of the tube over and pinch it tightly, then
remove the squeeze bulb. Now lift the tube clear of the water and let it
hang vertically.
4. What upward force is holding the water in the tube against the downward force
of gravity?
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5. Using what you’ve observed in question 4, devise a method to transfer water
from your water tank to the plastic cup using the soda straw and demonstrate
it to your instructor. Briefly explain your technique here.
Compressible and Incompressible Fluids
Now draw some water up into your veterinary syringe so that it is about half
full by drawing back the plunger while the tip is under water. Seal the end of
the syringe with your finger or thumb. Press hard on the plunger and
carefully observe the air and water inside the syringe.
6. As you push on the plunger, how does the pressure inside the syringe change
(increase/decrease/same)?
7. How is the pressure change inside the syringe related to the force you apply
to the end of the plunger and the area of the end of the plunger?
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8. Observe carefully the volume occupied by the air and the water as you press
on the plunger. How does the volume of the air change? The water?
9.
A fluid is said to be compressible if its density (and hence its volume, for a
fixed amount of fluid) changes with pressure and incompressible if its
density does not change with pressure. Based on your observations, classify
water and air (both fluids) as either compressible or incompressible. Explain
your reasoning.
Water _______________
Air ______________
Continuity in Fluid Flow
Make a note at where the water level is in your water tank. Hold the plastic
cup near the outlet hole on the water tank and note the height of the water in
the tank. Pull the nylon plug out and catch the stream of water exiting the
hole in the cup until the cup is 2/3 full then stop the flow of water out of the
tank by replacing the nylon plug into the hole.
10. Accounting for any small amount of water you may have spilled, how does the
amount of water in the cup compare with the amount of water that flowed out
of the tank?
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11. Pour the water in the cup back into the tank. How does the level of the water
in the tank now compare with the water level before you filled the cup, to
within the error caused by any water you may have spilled?
12. The principle of continuity says that the mass of a fluid must be conserved
as the fluid flows so that no fluid is lost or gained during the flow. Do your
results for questions 10 and 11 support this principle?
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The Cartesian Diver
Fill a soda bottle full of water. Insert the air-filled eyedropper into the bottle
pointed-tip down. Twist the lid on the bottle tightly making sure the bottle is
still full to the brim.
13. What happens when you squeeze the bottle? Discuss with your group what
you’ve observed and explain the effect using the concepts of pressure,
compressibility, density, buoyancy and Pascal’s Principle. (Hint: Pay attention
to the water level inside the eyedropper and review your observations and
answers for questions 6-9).
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Moving Fluids
Hold a sheet of paper horizontally and blow over the top of it.
14. Use the relationship between the pressure and speed in a moving fluid
predicted by Bernoulli’s equation to explain what you observe. (Hint:
Remember that a pressure difference across a surface produces a net force).
Briskly flip the washer horizontally off the edge of the table and observe its
motion.
15. What type of motion does the washer execute after being launched off the
edge of the table? (Hint: We studied this type of motion in a previous class).
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Next uncover the hole in the water tank and observe the motion of the stream
of water for a few seconds, then re-seal the hole.
16. Now consider the motion of the water stream as it exits the hole in the tank.
Consider a single drop of water in the stream to be a small mass m projected
horizontally out of the hole. How does the motion of this drop compare to the
motion of the washer?
Place the aluminum ruler in the bottom of the plastic tub so that the water stream
from the tank will land on or near it—this is to help you judge the distance the water
stream travels horizontally. With the water tank nearly full, uncover the hole in the
tank and observe the stream of water as the tank empties, paying careful attention to
how the horizontal distance the stream travels changes as the height of the water in
the tank decreases.
17. How does the distance the stream travels horizontally change as the level of
the water in the tank decreases?
18. Given that every drop of water in the stream always falls the same vertical
distance to the bottom of the tub, and hence always takes the same time to
fall into the tub, what quantity describing the horizontal motion of a drop of
water in the stream determines how far the stream of water will travel
horizontally before hitting the bottom of the tub?
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For every drop of water of mass m that leaves the hole in the tank with a
horizontal speed v, and hence a corresponding amount of kinetic energy
½ mv2, the principle of continuity ensures that an identical drop of water is
removed at the surface of the water located at a height h above the hole. As
each drop exits the hole, the water level in the tank therefore falls by exactly
one identical drop’s worth. The gravitational potential energy of a drop at the
top of the tank is mgh.
19. How is the amount of gravitational potential energy lost as the liquid level falls
by one drop’s worth related to the kinetic energy of an identical drop of water
simultaneously leaving the hole in the tank? State the principle that dictates
this relationship, and write a simple expression relating the height of the water
above the hole and the speed of the water exiting the hole. (Hint: You have
already done this calculation in a previous lab!)
Start water flowing from the tank through the long siphon tube into the
plastic tub, using your squeeze bulb to draw water down the tube and start
the flow. Holding the low end of the siphon tube horizontal vary its height and
observe the exit speed of the flowing water, as evidenced by the arc it makes
falling into the tub.
20. At what height relative to the water level in the tank does the flow through
the siphon cease? (Lab Tip: Hold the output end of the tube horizontally near
the ruler on the tank and move it up and down to find where this happens).
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21. Does the water’s speed increase or decrease as the output end of the siphon is
lowered relative to the water level in the tank?
22. Holding the output end of the siphon fixed near the bottom of the tub, vary
the distance the pick up end of the tube is inserted below the surface of the
water inside the tank. What effect does this have on the speed of the water
exiting the siphon?
23. The water in the pickup end of the siphon tube is actually flowing uphill.
What pushes the water up the tube? (Hint: Consider your answer to questions
3 and 4).
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Levitate the table tennis ball vertically with the hair dryer. Now tilt the
hair dryer toward the horizontal and see how close to horizontal you can
rotate the stream of air and still trap the ball. You can compete with other
groups!
24. Using the speed-pressure relationship from Bernoulli’s equation and the fact
that a difference in pressure across an object produces a net force, explain
how the ball is trapped in the flowing air.
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Everyday Applications
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When dams are built, they must be
reinforced at their base. You can see this
feature in dams, such as this one from
Australia. The angled base is strong
enough to support the higher pressure
at
the floor of the reservoir.
Siphons are frequently used to move
massive volumes of water easily (such
as in aquariums and swimming pools).
Flexible tubing filled with water (just like you used today) is used by contractors
to verify that a foundation is truly level.
Siphoning is a highly dangerous tool used by some to steal gasoline when
there are high gas prices.
Your ears pop when you change elevation in planes or cars
1. Many of you have probably experienced the very strong winds which
blow from Church Street, past Dennison Hall toward Randall Lab. One
very windy day I was walking along Dennison Hall toward the front steps
of Randall Lab. Just as I passed the door to Dennison, a very strong
gust of wind blew through and the door to Dennison, which had not
latched, swung violently open.
Explain what happened using the
relationship between speed and pressure in a moving fluid described by
Bernoulli’s equation. (Hint: Review your analysis of the levitated table
tennis ball and the air-over-paper experiments).
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2. Describe a real-world application for the liquid transfer technique you
developed in question 5. (Hint: Think Biology or Chemistry lab).
3. Given that atmospheric pressure exerts 22 tons of force on every square
meter of our bodies, why are we not crushed or made uncomfortable by
the large pressure forces that act on us?
(Hint:
Consider your
observations and answers for questions 6-9).
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Summary
1. Pressure is defined as force per unit area.
2. Pressure is a scalar, area is a vector.
3. Compressible fluids change their density with pressure, incompressible
fluids do not. Air is a compressible fluid, water is an incompressible fluid.
4. The principle of continuity states that no fluid is lost or gained as the fluid
flows.
5. Pascal’s Principle states that pressure is transmitted uniformly throughout a
fluid and to the walls of the vessel containing the fluid.
6. Pascal’s Law states that the absolute pressure at the bottom of fluid column
of height h is given by Pabsolute  Patmospheric   gh .
7. Gauge pressure is defined as the additional pressure relative to
atmospheric pressure. The gauge pressure at a depth h in a fluid is therefore
Pgauge   gh
8. Application of the Work-Energy Theorem (energy conservation) to a moving
fluid yields Bernoulli’s equation.
9. For a fluid flowing in a level pipe, Bernoulli’s equation, and hence energy
conservation, dictates that pressure in a fluid decreases as the speed of
flow increases.
10.The speed of a fluid exiting a hole in a vessel or exiting a siphon is dictated by
energy conservation and is determined by the height of the fluid level
above the exit hole or siphon output.
11. The exit speed from a siphon does not depend on the depth the siphon is
inserted below the surface of the fluid.
12.The difference between atmospheric pressure at the surface of a fluid and
the lowered pressure at a point in the moving fluid higher than the surface
drives the flow of fluid uphill in a siphon.
Final Clean-up
Please prop up your tub to drain into the Homer bucket and wipe up any spilled water
with your sponge/rag. Pease empty your Cartesian diver water into the bucket and
remove the eye dropper from the bottle.
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More Everyday Applications
Suction Cups
When a suction cup is pressed to a smooth surface two things happen.
First, the air is evacuated from the concave chamber. Once most of the air is
evacuated, there is air pressure disequilibrium. The ambient air pressure is greater
than the pressure inside the chamber and therefore exerts a force on the suction cup.
Second, the force exerted by the greater ambient air pressure presses the cup onto
the surface, forming a hermetic seal (impenetrable to air). A hermetic seal does not
allow air to pass between the inner chamber and the ambient, so the disequilibrium
does not correct itself.
This is why the suction is successful.
Figure 1: The left figure is the suction cup before being pressed. The inside
and outside pressures are the same, so the cup can be easily removed. The
right figure is the suction cup after being pressed. The inside and outside
pressures are not the same, and so the cup has suction to the surface.
If a person wants to remove a suction cup from a smooth surface they must pull with a
force greater than the pressure difference between the chamber and the ambient air.
Force (F) is equal to pressure (p) multiplied by the area (A):
F  p A
This means that as the area increases, the force increases. That is why with a larger
suction cup, the force you need to pull it off a surface is greater than with a smaller
suction cup.
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Surface Level Equilibrium
You observed with your U-shaped tube that the surfaces of all connected bodies of
water exposed to the ambient air end up level with one another.
Now, pressure is exerted in every direction at any given point: up, down, and side-toside. Consider what would happen if one of the columns of water were higher than the
other.
Figure 2: In this U-Tube, the pressure is shown with arrows. The arrows
indicate that pressure is exerted in all directions at any given point. In the
left hand figure, the right tube is exerting a greater pressure than the left,
and so the water level will shift to the left. In the right hand figure, the levels
are equilibrium, so pressure does not favor a direction.
Straws
Most young children master the skill of sipping on soda through a straw. Few probably
know that they are mimicking suction cups. Ambient air pressure is everywhere, ready
to push soda into your belly. All it needs is a little incentive, like pressure
disequilibrium. Human’s can create reduced pressure in their mouths, and the soda is
just caught in the middle. The ambient air pushes the soda into your mouth until the
pressure is at equilibrium, at which point you can repeat the process.
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