Fluids I
Level : Physics I
Teacher : Kim
1. Density
One of the properties of any substances (solids, liquids and gases) is the measure of how tightly
the material is packed together. This property is called density.
Density is a measure of how much matter is squeezed into a given space, that is, the amount of
mass per unit volume.
𝑚𝑎𝑠𝑠
density =𝑣𝑜𝑙𝑢𝑚𝑒[kg/m3]
Q1) Order the following materials from lowest to greatest according to their densities.
water
interstellar-space
blood
Earth’s core
Sun’s core
Earth’s crust
seawater
black-hole
Q2) i) What is the density of an object of mass 12kg and a volume of 4m3?
m=12kg,
volume=length×width×height = 4m3
ii) What is the mass, volume and density if we break the object in half?
2. Pressure
Demo1) Hold a weight(50g) and a sponge ball.
i) Observe which object ‘feels’ heavier.
a) Weight feels heavier!
b) Sponge ball feels heavier!
ii) The weight of the sponge-ball is actually (
)g
Demo2) Hold a book in three different ways as below. Which case seems ‘heaviest’?
i) flat on your hand
ii) upright on your hand
iii) only the corner on your hand
How much ‘press’ we feel from the book depends in the area of contact for each case. That is, the
amount of force per unit area is called pressure.
𝑓𝑜𝑟𝑐𝑒
𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎
pressure=
𝐹
P=
𝐴
where P is the pressure and A is the area over which the force acts
The unit for pressure is pascal(Pa). One Newton per square meter is equal to one pascal. That is,
1N/m=1Pa
Q3) A cube is lying on the floor. If the mass of the cube is 2kg,
find the pressure the cube is exerting on the surface of the floor.
(weight is Fg=mg, where g=9.8m/s2)
0.2m
0.2m
0.2m
3. Liquid Pressure according to depth
Liquid has weight(=force), so it must also exert pressure.
Q4) Compare the following two situations.
Case1) You are swimming 1 meter deep in an Olympic size pool
Case2) You are swimming 1 meter deep in an ocean
In which case would you feel more pressure?
- Liquid pressure depends only on the density and the depth of the liquid, not on the shape or size
of its container.
- Liquid pressure does not depend on the amount of liquid
- Liquid does not compress, so the density at the surface or bottom of a lake approximately the
same
Pressure due to liquid = density × depth
Q5) Why dams are built thicker at the bottom?
Large, but shallow lake
Small, but deep lake
4. Buoyancy
Why do object weigh less in water than on air?
When an object is submerged in water, the water exerts an upward
force that is opposite to the downward force Fg (weight). This upward
force is called buoyant force( Fb )
Try pushing a volley ball into water. The water will try to ‘push back’
on the volley ball back up to the surface. That ‘pushing back’ force is
the buoyant force Fb
Fb
Fg
Q6) Explain why water exerts an upward force on objects in the water. (hint: remember that
liquid pressure exerted on an object varies according to depth only)
Q7) Buoyant force and weight are both forces. If one is acting greater than the other on an object,
the object will move in that direction. Connect the statement for each case.
If the weight of a submerged object is greater than the
float
buoyant force, then the object will
the weight of a submerged object is less than the buoyant
stay still
force, then the object will
the weight of a submerged object is equal to the buoyant
sink
force, then the object will
Q8) A bowling ball has a diameter of 21.8cm. A volley ball has a diameter of 20.7cm to 21.3cm.
If the two balls are pushed completely under water and then released, the volleyball will float
back up while the bowling ball will sink. Which statement is true?
a) the buoyant force acting on the bowling ball is less than the volleyball
b) the buoyant force acting on the bowling ball is greater than the volleyball
c) the buoyant force acting on the bowling ball is similar than the volleyball
The following statement is false.
‘ The buoyant force acting on a volleyball is much greater than the buoyant force acting on a
bowling ball’
‘ The buoyant force that acts on a completely submerged object is determined by the weight or
mass of the object
‘ The buoyant force that acts on a completely submerged object equals the weight of the object’
To further understand buoyancy, we need to see what happens when an object is placed in water.
the amount of liquid
- If a stone is placed in a container of water,
displace
the water level will rise because the stone
=volume of the stone
‘pushes’ the water aside.
- How much water is pushed
away(=displaced) is determined by the
volume of the object, and irrelevant to the
weight, mass, color, smell etc, of the object.
- The amount of water displaced is equal to
the volume of the stone
- A completely submerged object always displaces a volume of liquid equal to its own volume.
And the more liquid the object displaces, the stronger the buoyant force.
5. Archimede’s Principle
*~An immersed object is buoyed up by a force equal to the weight of the fluid it displaces.
Archimede’s principle = Newton’s 3rd law
If you put something in water that pushes 100N of water out of the way(=displaces 100N weight
of water), then the water pushes back with a force of 100N. The buoyant force is always equal
and opposite to the weight of the water you displace
What does the above principle mean?!!
- A liter is a measure of volume. 1-liter is equal to the volume of a
cube with 10cm sides
10cm
- If you immerse 1-liter container into water, whether the container is
empty or filled with anything, the container will displace 1 liter
volume of water,
10cm
10cm
- If we weigh that 1-liter of water on a scale, it will weigh 9.8N. Since the buoyant force is equal
to the weight of water being displaced, the buoyant force acting on the 1-liter container filled with
anything will always be 9.8N in water
- If we immerse an empty 1-liter container in water, the empty container will float since the
buoyant force is greater than the empty container.
- If we fill the 1-liter container with water and immerse it into water, the container will stay still
in the water, since the buoyant force is equal to the water-filled container.(that is, if we assume
the mass of the container itself is very light)
- If we fill the 1-liter container with mercury(which is more dense and heavier than water) and
immerse it into water, the container will sink, since the buoyant force is less than the mercuryfilled container.
- If we fill the 1-liter container with water and immerse it into pool of mercury, the container will
float, since the buoyant force is greater than the water-filled container.
- If we fill the 1-liter container with mercury and immerse it into pool of mercury, the container
will stay still, since the buoyant force is equal to the water-filled container.
A liter of water has a mass of 1kg and weighs 9.8N. Any object with a volume of 1 liter will
experience a buoyant force of 9.8N when fully submerged
-
If we immerse a sealed 1-liter container halfway into water, it will displace half a liter of
water.
- If we immerse it all the way, it will be buoyed up by the weight of a full liter of
water(about 9.8N)
- The buoyant force will equal the weight of 1 liter of water at any depth( **water is
incompressible, so density is the same in any depth)
- The container will displace the same volume of water, and hence the same weight of
water at any depth
- The weight of this displaced water( not the weight of the submerged object!!) is the
buoyant force
Caution!! The buoyant force that acts on a submerged object is irrelevant of the mass or
weight of that object. It is only determined by the volume of the object.
Q9) A 1-liter container filled with mercury has a mass of 13.6kg and weighs 133N. When it is
submerged in water, what is the buoyant force on it? Will it float, sink or stay still in the water?
Q10) A block is held suspended beneath the water in
three positions. In which position is the pressure the
greatest? In which position is the buoyant force the
greatest? Explain!!
A
B
C
Additional Question
A 1-liter container filled with water has a mass of 1kg and weighs 9.8N. A 1-liter container filled
with mercury. A 1-liter container filled with mercury has a mass of 13.6kg and weighs 133N.
Use the information above to answer the following questions.
1. What is the buoyant force acting on an empty 1-liter container when submerged into water?
Will it float, sink or stay still in the water? Justify your answer~!
2. What is the buoyant force acting on a 1-liter container filled with mercury liquid when
submerged into water? Will it float, sink or stay still in the water? Justify your answer~!
3. What is the buoyant force acting on an empty 1-liter container when submerged into mercury
liquid? Will it float, sink or stay still in liquid mercury? Justify your answer~!
4. What is the buoyant force acting on a water-filled 1-liter container when submerged into
mercury liquid? Will it float, sink or stay still in liquid mercury? Justify your answer~!
6. Floatation
When primitive people observed that wood floats on water, they made their boats of wood. Could
they have conceived of an iron ship?
The idea of floating iron might be seem strange and impossible at that time since iron sinks, but
today we see huge ships made of iron that floats.
*~How to make iron float
Consider a solid 1-ton block of iron. Iron is nearly 8 times denser than water, so a block of iron
will sink. So how can we make that piece of iron float?
Since iron is so dense, the weight of water it displaces will be no match for the weight of the iron.
That is, the buoyant force is less than the weight of the piece of iron. = sink
However, if we shape the iron into a bowl shape, we can increase the amount of water it
displaces. This will increase the buoyant force acting on the iron.
float!!
sink!!
*The principle of floatation*
A floating object must displace a weight of fluid equal to its own weight
=>Every ship must be designed to displace a weight of water equal to its own weight
Ex) A 10000 ton ship must be built wide enough to displace 10000 tons of water before it
sinks too deep below the water