1. L-14 Fluids [3] Fluids at rest Fluids in Motion  Fluid Dynamics
Why things float  Archimedes’ Principle
Fluids in Motion  Fluid Dynamics
Hydrodynamics
Aerodynamics

2. Buoyancy – why things float
TITANIC
The trick is to keep the water on the outside of the ship, and
to avoid hitting icebergs (which also float), and
are easy to miss since 90 % of it is submerged.

3. The area of the hole in the Titanic’s bow
was just over a square meter.
It sank in 160 minutes.

4. Buoyant Force FB Pressure increases with depth submerged object
that has a mass
density ρO
The density of the
water is ρW
PTopA
F = P  A h
PBottomA W

5. Archimedes’ Principle
PBottomA > PTopA
A buoyant force FB equal to the weight of displaced water is exerted on a submerged object.
The object sinks to the level where FB = W
every liter of water displaced
provides a buoyant force of 10 N FB W

6. Archimedes principle The buoyant force on an object in
a fluid equals the weight of the
fluid which it displaces.
this works for objects in water
helium balloons (density of He = 0.18 kg/m3, about 7 times less dense than air)
hot air balloons  the density of
hot air is lower than the density of cool
air so the weight of the cool air that is
displaced is higher than the weight
of the balloon

7. Will it float?
The buoyant force is always there whether the object floats or not
The object will float if the buoyant force is big enough to support the object’s weight
The object will displace just enough water so that the buoyant force = its weight
If it displaces as much water as possible and this does not equal its weight, it will sink.
Objects that have a density less than water will float- when fully submerged, they weigh less than the water, so the water supports them
water weighs about 10 N per liter

8. The weight of displaced
Floating objects
lighter object
heavier object
too heavy
The weight of displaced
water is less than the
weight of the object

9. example problem
An object having a volume of 6 liters and weighing W = 30 N is placed in a tank of water. What will happen? Will it sink? Will it float? What fraction of its volume will be submerged if it floats?
If the object were completely submerged, the buoyant force would be FB, max = 10N/liter x 6 liters = 60 N
thus, the object will float with half of its volume submerged, so that FB = W = 30 N W FB

10. Oil Tankers
empty
tanker
full
tanker

11. Floating in a cup of water
Only a thin layer of
water around the hull
is needed for the ship
to float!

12. Why does ice float?
Water, the most plentiful substance on earth is also one of the most unusual in its behavior in that it expands when it freezes.
Since it expands, the density of ice is slightly less than the density of water (917 kg/ m3 as compared to 1000 kg/ m3 for water). So the part of the iceberg above the surface is less than 10% of the total volume.

13. Place your bets! When the ice cube melts will: the water spill out, or
the water level stay the same, or
the level go down ????????
ice cube
Answer: The level stays the same.
Ice is less dense than water, so that
the volume occupied by the ice is
exactly big enough to hold the
volume of melted water that was
not submerged!

14. Fluid Flow
The physics of fluid flow was worked out by Daniel Bernoulli
He was born in Switzerland in 1700
He was one of 5 brothers and came from a large family of mathematicians and scientists.

15. fluid flow example – leaky cup
Pressure increases
with depth, so the
speed of water leaking
from the bottom hole is
larger than that from the
higher ones.

16. How do we measure fluid flow?
We see how much comes out in some time interval
Time how long it takes to fill the bucket, say 30 seconds
the flow rate is then 1 bucket say per 30 seconds
in other words volume per unit time
gallons per min (gpm), liters/s, cubic feet per min (cfm), gpf,
or m3/s  volume flow rate

17. Volume flow rate
If the water comes out of a tube of cross sectional area A with a flow speed u the volume flow rate is
volume flow rate = u  A (m/s m2)
To measure u just see how long it takes to fill a gallon jug from a hose and measure the diameter of the hose.
m3/s

18. Mass flow rate
We could also measure how much mass comes out per unit time – kg/s for example
if you are using a fluid of density  coming out of a hose of cross sectional area A with speed v the mass flow rate is
mass flow rate =   u  A

19. What makes water flow? Stanton, IA Montgomery Co. gravity
by placing the water up high the pressure at the bottom is high enough to supply water to all parts of town that are lower than the tower
Stanton, IA
Montgomery Co.

20. Pressure differences P2 P1 a pressure difference must be established
across the ends of the pipe to push the water
along.  P2 must be greater than P1
This pressure difference can be set up by
a water pump.

21. Water does not disappear!
If water goes in one end of a pipe it must come out the other end (if there are no leaks of course. Sounds obvious, but it has a number of interesting consequences!
This applies to pipes that have constrictions also.
v1, A1
v2, A2

22. Continuity of flow
since whatever goes in must come out we have that the incoming flow rate – outgoing flow rate or
v1 A1 = v2 A2
thus the fluid in the narrow part of the tube must flow FASTER that the fluid on the left.
Cardiologists use this to determine if arteries might be clogged.

23. Other examples - the nozzle effect
you use this principle whenever you hold your finger over the end of the hose to make the water spray farther.

24. An amazing thing about moving fluids
The pressure in a moving fluid is less than the pressure in a fluid at rest!  this is Bernoulli's principle.
Where a fluid moves faster its pressure is lower, where it moves slower, its pressure is higher.
As we will see, this is the principle that makes airplanes work.

25. The Venturi Meter

26. wind roof Bernoulli applies to household plumbing too! air vent
When the wind is
really blowing, watch
the water level in the
toilet go up and down
sewer

28. Prairie dogs know how to use Bernoulli's principle

29. “atomizers”
fine droplets of liquid (not atoms) are sprayed from this device using the Bernoulli effect