Hydrostatics

Physics CLIL 1D a.s. 2014-2015
HYDROSTATICS

the branch of
fluid mechanics
that studies
fluids
at rest
HYDROSTATICS

Liquid and aeriform substances
(gasses and vapours) are fluids
What is a FLUID?
A fluid is a substance that
can
flow

Water is a fluid
Oil is a fluid
Smoke is a fluid
Air is a fluid

Fluids conform to the boundaries
of the container in which they are
placed

At a given temperature, each substance has its own
density
which is
the ratio of a given mass of the substance and its volume:
DENSITY
𝒅𝒆𝒏𝒔𝒊𝒕𝒚 =
𝒎𝒂𝒔𝒔
𝒗𝒐𝒍𝒖𝒎𝒆
=
𝒎
𝑽
𝑆𝐼 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡:
𝒌𝒈
𝒎 𝟑

Normally, the higher is the temperature
of a substance the smaller is its density
becouse its volume increases with
temperature.
DENSITY

PRESSURE

Pressure is the magnitude F of a force acting perpendicular to a
surface divided by the area S of the surface over which the force acts.
PRESSURE
𝑷 =
𝑭⊥
𝑺
𝑆𝐼 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡:
𝑵
𝒎 𝟐 = 𝑷𝒂 (𝑝𝑎𝑠𝑐𝑎𝑙)

PRESSURE
𝐹
𝐹⊥
𝑆
Force
Perpendicular force
Surface

PRESSURE
Pressure is not a vector
quantity but a scalar quantity

PRESSURE
For a given pressure Force and Area are
directly proportional
𝐴 (𝑚2
)
𝐹 (𝑁)

PRESSURE
For a given Pressure Force and Area are directly proportional
Weight=10N
Area=1𝑚2
Pressure=
𝑤𝑒𝑖𝑔ℎ𝑡
𝑎𝑟𝑒𝑎
=
10𝑁
1𝑚2 = 10𝑃𝑎
Weight=20N
Area=2𝑚2
Pressure=
𝑎𝑟𝑒𝑎
=
20𝑁
2𝑚2 = 10𝑃𝑎

PRESSURE
For a given Force, Pressure and Area are inversely proportional
𝐴 (𝑚2)
𝑃 (𝑃𝑎)

PRESSURE
Weight=10N
Area=1𝑚2
Pressure=
𝑎𝑟𝑒𝑎
=
10𝑁
1𝑚2 = 10𝑃𝑎 Pressure=
𝑎𝑟𝑒𝑎
=
10𝑁
2𝑚2 = 5𝑃𝑎
For a given Force, Pressure and Area are inversely proportional
Weight=10N
Area=2𝑚2

PRESSURE
For a given Area, Pressure and Force are directly proportional
𝐹 (𝑁)
𝑃 (𝑃𝑎)

PRESSURE
Weight=10N
Area=1𝑚2
Pressure=
𝑎𝑟𝑒𝑎
=
10𝑁
1𝑚2 = 10𝑃𝑎
Weight=20N
Area=1𝑚2
Pressure=
𝑎𝑟𝑒𝑎
=
20𝑁
1𝑚2 = 20𝑃𝑎
For a given Area, Pressure and Force are directly proportional

PRESSURE
Now try to answer!

PRESSURE
Why does a sharp knife
cut better than a dull
knife?

PRESSURE
The diagram at right shows a sharp knife and a dull knife in
contact with a surface (maybe a nice, juicy steak!).
Notice that the sharp knife has a very small area of contact
with the surface, while the dull knife has a much larger area
of contact.
If both knives are pushed down with the same force, the
sharp knife will exert a much greater pressure on the
surface than the dull knife - and pressure cuts.
So, if you are "stuck" with a dull knife, you have to exert
much more force in order to generate enough pressure to
cut your steak.

PRESSURE
Why do people have to
use ice skates?

PRESSURE
The downward force that you exert on the
ice (assuming you are standing on two
feet) would be half of your weight.
Notice, however, that the shoe distributes
the force over a much larger area than the
skate does. This means that the skate
exerts a much higher pressure on the ice
than the shoe does - it is this high pressure
that makes ice skating possible!

PRESSURE
Why a karate chop is much
more effective than an
open-handed slap?

PRESSURE
Because a reduction of surface area increases net
pressure.
If one were to slap a board squarely with one's palm,
the only likely result would be a severe stinging pain
on the hand.
But if instead one delivered a blow to the board, with
the hand held perpendicular the board could be split
in two.
In the first instance, the area of force exertion is large
and the net pressure to the board relatively small,
whereas in the case of the karate chop, the surface
area is much smaller—and hence, the pressure is
much larger.

PRESSURE
Why snowshoes are much
more effective for walking
in snow ?

PRESSURE
Sometimes, a greater surface area is preferable.
Thus, snowshoes are much more effective for
walking in snow than ordinary shoes or boots.
Ordinary footwear is not much larger than the
surface of one's foot, perfectly appropriate for
walking on pavement or grass. But with deep
snow, this relatively small surface area increases
the pressure on the snow, and causes one's feet
to sink. The snowshoe, because it has a surface
area significantly larger than that of a regular
shoe, reduces the ratio of force to surface area
and therefore, lowers the net pressure

PRESSURE
syringe
hammer
nail
pushpin

Physics at home
PRESSURE

What you need:
- 1 carton of milk (closed); a dish; some flour, a scale, a ruler
What to do:
1. weight the carton of milk
2. measure the three dimensions (a, b and c) of the carton
3. calculate the area of each side (axb, bxc and axc) of the carton
4. place the carton on a table and calculate the three different pressures
it exerts on the three different contact surfaces between the table and
the carton
5. Pour the flour into the dish and place carefully the carton over the
flour, firstly with the largest size in contact with the flour , then the
medium size and eventually the smallest size (before placing the
carton on the flour, flatten the surface of the flour)
What do you notice?
How can you explain?
PRESSURE

PRESSURE
Pascal’s principle
Any change in the pressure applied to a
completely enclosed fluid is transmitted
undiminished to all parts of the fluid and the
enclosing walls
Blaise Pascal
(1623-1662)

PRESSURE
Pascal’s principle
When the syringe is filled
with water, pushing the
plunger water comes out
from all nozzles with equal
speed perpendicularly to
the surface of the container

PRESSURE
A Pascal’s principle application
THE HYDRAULIC PRESS
experiment

PRESSURE
STEVIN’S LAW
Simon Stevin (1548 – 1620)
The pressure at a point in a liquid
in static equilibrium depends only
on the depth at that point:
𝑷 = 𝑷 𝟎+dgh
Where 𝑷 𝟎is the external pressure on the surface of the
liquid, h is the depth, g is the gravity acceleration and
d is the liquid density

PRESSURE
STEVIN’S LAW

PRESSURE
STEVIN’S LAW APPLICATIONS
𝑪𝒐𝒎𝒎𝒖𝒏𝒊𝒄𝒂𝒏𝒕 𝒗𝒂𝒔𝒔𝒆𝒍𝒔 (𝒗𝒂𝒔𝒆𝒔)
Given a set of two or more connected containers containing a
homogeneous liquid, when the liquid settles, it balances out to the same
level in all of the containers regardless of the shape and the volume of the
containers

PRESSURE
𝑷𝒂𝒔𝒄𝒂𝒍′
𝒔 𝒃𝒂𝒓𝒓𝒆𝒍 𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕

PRESSURE
Watch the video

PRESSURE
Hydrostatic pressure inside the
water in a dam or a swimming pool
increases with depth according to
Pascal’s principle and Stevin’s law.
That is the reason of the trapezoidal shape of
walls in dams and swimming pools

PRESSURE
ℎ1
ℎ2
𝑑2𝑑1
ℎ2 > ℎ1 → 𝑃2 > 𝑃1 → 𝑑2 > 𝑑1

ATMOSPHERIC PRESSURE
The atmosphere of Earth is a layer of gasses
surrounding the planet Earth that is retained by Earth's
gravity.
Three quarters of Earth atmosphere is within about 11 km
from the planet surface.
The atmosphere becomes thinner and thinner with
increasing altitude, with no definite boundary
Although its density is very small, it exerts a great force
over all the objects on the Earth surface

Atmospheric pressure is the force exerted per
unit of area on the surface of the Earth by the
column of air extending vertically above it.
The average atmospheric
pressure at sea level is 1
standard atmosphere
(atm)=101.3 kPa

70cm
(at sea level)

h = 70cm (at sea level)

PRESSURE
BUOYANCY
Buoyancy is an upward force exerted by a fluid that
opposes the weight of a partially or completely immersed
object.

PRESSURE
ARCHIMEDES’ PRINCIPLE

PRESSURE
𝒃𝒖𝒐𝒚𝒂𝒏𝒕 𝒇𝒐𝒓𝒄𝒆 = 𝒇𝒍𝒖𝒊𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 ∙ 𝒈 ∙ 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒅𝒇𝒍𝒖𝒊𝒅
𝑭 𝑩 = 𝒅 𝒇 ∙ 𝒈 ∙ 𝑽 𝒇

PRESSURE
𝒇𝒍𝒖𝒊𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 > 𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 → 𝒕𝒉𝒆 𝒐𝒃𝒋𝒆𝒄𝒕 𝒇𝒍𝒐𝒂𝒕𝒔
𝒇𝒍𝒖𝒊𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 < 𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 → 𝒕𝒉𝒆 𝒐𝒃𝒋𝒆𝒄𝒕 𝒔𝒊𝒏𝒌s
𝒇𝒍𝒖𝒊𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 = 𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 → 𝒕𝒉𝒆 𝒐𝒃𝒋𝒆𝒄𝒕 nor floats nor
sinks

PRESSURE
air ballon
submarine
aircraft carrier
For a fully submerged object, Archimedes'
principle can be reformulated as follows:
Immersed object’s apparent weight =
weight of the object – weight of the displaced
fluid

Hydrostatics

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