16 pius augustine fluid pressure and flotation

1
Fluid pressure and Flotation

FLUID MECHANICS
A substance which can flow is called
a fluid.
Deforms under even the smallest
shear or tangential stress.
Include liquid and gas (vapour)
Dr. Pius Augustine, S H College, Kochi

Ideal liquid or inviscid fluid
Incompressible and non viscous
Incompressible: density of liquid is
constant, and is independent of the
variations in pressure.
Non viscous: no friction between adjacent
layers .ie . Forces between surfaces is
perpendicular to surface.

Thrust
Total normal force acting on a
surface is called thrust.
independent of area
Vector quantity
SI unit is N Dr. Pius Augustine, S H College, Kochi

Density and R.D
• Density = mass / volume unit
kg/m3
•R.D (Specific gravity)
= D/ D(water at 40C)
• 1000kg/m3 = 1g/cm3
• In CGS, numerical value of density
and relative density are same.

Pressure = F / A
Thrust per unit area.
scalar qty.
SI unit is N/m2. (Pa)

Fluid Pressure
Pressure exerted by a fluid on the
bottom as well as the wall of the
container.
Fluid exert press at all points and in
all directions, within it.

Give unit of pressure in terms of base
units.
F/A
Kgms-2/m2
Kgm-1s-2

Static pressure
Independent of direction
in an immovable (static)
fluid.

Dynamic pressure :
Flowing fluid applies additional pressure on
surfaces perpendicular to the flow
direction, while having little impact on
surfaces parallel to the flow direction.
This directional component of pressure in a
moving (dynamic) fluid is called dynamic
pressure. Dr. Pius Augustine, S H College, Kochi

Total pressure or Stagnation pressure
An instrument facing the flow
direction measures the sum of
the static and dynamic pressures

Units of pressure
• Units : Pa or N/m2
• Bar = 105 Pa
• 1torr = 1 mm of Hg
atm , psi, psig , psia
Absolute pressure is always greater than or equal to zero
Gauge pressure { P absolute – P atm } can be –ve.
One psi = 6894.75728 Pa
1 centi Hg = one cm of Hg
= 1333.2239 N/m2.

Pressure gauges
Devices for measuring
pressure of a liquid or
gas.

How does the pressure exerted
by a thrust depend on area of
surface on which it acts ?
Explain with a suitable
example.

A brick (weight = 10N) having dimension
20cm x 10cm x8cm .
It can be placed on the floor in three different
ways having 3 different areas of contact. P ?
i) Area of contanct A1 = 200cm2,
P1 = 10/200 = 0.05 N/cm2.
ii) A2 = 160 cm2……
iii) A3 = 80cm2…….

Why are sleepers used below the rails ?
To increase the cross-sectional
area.
It reduces the pressure due to
weight of the train on the rails.

One pascal
Pressure exerted by 1N
normal force on 1m2
area is 1Pa.

“ Force accelerates, pressure cuts” .
Comment
Hint: sharpness of knife

Sharp knife cut better, but a blunt knife
not. Why ?
Sharpness reduces area of
contact.
ie. pressure will be very large
and cuts.
Same is the case with sharp pin.

Bags and suitcase are provides with broad
handle. Explain.

Why is it more comfortable on a soft bed than
on a floor?
Both bed and floor balances wt of the
person.
Mattress conforms the shape of the
body and hence larger area than floor
does.
ie. Mattress exert less press. (presure
cuts)

What is gradient of pressure ?
Change in pressure with distance is
called gradient.
Used in metereology or climatology.
P/x = F/AX = F/V is called force density .
(unit N/m3)

Find the mass and wt of the air in a living
room with 4 x 5 m2 floor and a ceiling
3m high.
What is the mass and wt of equal volume
of water.
Density of air = 1.29 kg/m3.
Density of water = 1000 kg/m3.

Atmospheric pressure
Thrust exerted on unit
area of earth surface due
to column of air is called
atmospheric pressure.Dr. Pius Augustine, S H College, Kochi

Press exerted by a liquid column at depth h
below free surface P = hdg

Press exerted by a liquid column at depth h
below free surface P = hdg
d – density of liquid.
A point at a depth ‘h’ below the free surface.
Imagine cylindrical column of liquid as shown.
Thrust on the surface PQ
= Wt of cylindrical liquid column = Ahdg
Pressure = Thrust /area
= Ahdg /A
= hdg.

State three factors on which the pressure
at a point in a liquid depends?
Depth from the surface.
Density of liquid
Acceleration due to gravity.

Is blood pressure same at head and feet?
Explain.

How does the pressure at a certain depth in sea
water differ from that at the same depth in river
water? Explain.
If depth and ‘g’ are constants, P is
directly proportional to density.
Since sea water is denser, pressure will
be large compared to river water for
the same depth. Dr. Pius Augustine, S H College, Kochi

• Pyknometer : Instrument used to measure the
density and co efficient expansion of liquids
• Sphygmomanometer : common type of blood
pressure gauge
Diastolic : 80 torr , systolic : 130 torr
• Bourdon gauge : Tyre pressure gauge
• Hypsometer : instrument to measure height above
sea level

A bullet is fired into a sealed water filled vessel .
What will happen?
Give reason .

Prepare a note on blood
pressure variations and
symptoms.
Also life styles to correct it.

Explain why gas bubble released at the bottom of a
lake grows in size as it rises to the surface of the
lake?
Boyle’s law for gas PV = constant.
Well under water pressure is comparatively high
(pressure increases with depth).
As the bubble comes up , depth decreases and
pressure decreases, which in turn causes
increase in the volume making PV = constant.

A dam has broader walls at the bottom
than at the top. Explain.
Pressure increases with depth, and also
liquid exerts pressure in all directions.
So to withstand large pressure at the
bottom, walls at the bottom is made
broader.

Why do sea divers need special protective suit ?
Total pressure exerted on the
diver’s body becomes much more
than his blood pressure.
To withstand it, he needs a special
protective suit.

Pneumatics
Is the use of pressurised gas to
affect mechanical motion.
Eg: air brake

Laws of liquid pressure
i. Pressure inside a liquid increases with
Depth.
ii. same in all Directions about a point in a
liquid.
iii. Increases with Density of liquid.
iv. P same at all points on a Horizontal
plane, in a stationary liquid.
v. Liquid seeks its own Level.

Pressure measurement
Instruments used to
measure pressure are
called pressure gauges
or vacuum gauges.Dr. Pius Augustine, S H College, Kochi

Absolute pressure is zero
referenced against a perfect
vacuum, so it is equal to
gauge pressure plus
atmospheric pressure.

Gauge pressure is zero referenced
against ambient air pressure, so it
is equal to absolute pressure
minus atmospheric pressure.
Negative signs are usually omitted.

Differential pressure is
the difference in
pressure between two
points.

Manometer
A Manometer is a
device to measure
pressures

How does the liquid pressure on a diver
change if ..
i) Moves to a greater depth
Increases.
ii) Moves horizontally
no change.

Blaise Pascal 19.06.1623 - 19.08.1662

Pascal’s law – transmission of liquid pressure
States that the pressure exerted
anywhere in a confined liquid
is transmitted equally and
undiminished in all directions
throughout the liquid.Dr. Pius Augustine, S H College, Kochi

If pressure at some point of a
confined liquid is increased,
the pressure at all other points
of liquid must also increase by
the same amount.

Applications of
Pascal’s law
Principle of hydraulic machine

F1 / A1 = F2/A2
Small force on small piston appear as
large force on large piston.
Liquid is incompressible,
Small force on small piston makes it move
through a large distance
while large piston moves through a small
distance.

A1d1 = A2 d2
or
A1 /A2 = d2/d1.
F1/F2 = A1/A2 = d2/d1.

Uses of hydraulic press :
1. Pressing cotton bales and goods, quilts,
books etc .

2. Extracting juice of sugarcane, sugar beet
etc.

3. Squeezing the oil out of linseed and
cotton seeds.

4. Engraving monogram on goods.

Hydraulic jack or lift.
Used for lifting heavy vehicles such
as cars, trucks etc in service
stations for repair.
Works based on principle of
hydraulic machine.

Construction
Two cylindrical vessels P and Q
connected to each other by a tube R
having a valve.
Piston in narrow cylinder is attached to
a lever and that in large cylinder is
attached to a platform for lifting the
vehicle.
Vessel is filled with liquid. (say water)

Working
On pressing the handle, valve opens
and platform will be lifted, and the
process will be continued until,
desired lift of the vehicle is
reached.
Valve will be closed due to the wt of
the vehicle.

Hydraulic brakes
Used in cars works on Pascal’s law.

A hydraulic press with the larger piston of
diameter 35cm at a height of 1.5m relative to
the smaller piston of diameter 10cm. The mass
on the smaller piston is 20kg. What is the force
exerted on the body by the larger piston ? The
density of oil in the press is 750 kg/m3.
• Hint : P small - P big = hdg
• Solving : F big = 1.3 x 103 N

Two vessels A and B have same base area.
Equal volumes of a liquid are poured in the
two vessels to different height hA and hB (>
hA).
In which vessel, the force on the base of
vessel will be more.
• Hint : Force same , pressure different

A hydraulic auto mobile lift is designed
to lift cars with a maximum mass of
3000 kg. The area of cross section of the
piston carrying the load is 425cm2.
What maximum pressure would the
smaller piston have to bear ?

A U-tube contains water and
methylated spirit separated by
mercury. The mercury column in the
two arms are in level with 10cm of
water in one arm and 12.5 cm of spirit
in the other. What is the R.D of spirit.

A vertical tube contains water to a height ……
Given Solution
h= 1.5m d = 1000 SI
g = 9.8 N/kg
A = 10-2m2.
P = hdg = 1.5 x 1000 x 9.8 = 1.47 x 104 Pa
Thrust = P A = 1.47 x 104 x 10-2
= 147 N
Prepare a question which suits this?

a) calculate the height of . …
b) What conclusion…
Given the solutions
a) hMercury = 70 cm dMercury = 13.6 g/cc
hWater = ? dwater = 1g/cc
hMdM = hWdW.
hW = 70 x 13.6 / 1 = 952 cm .
b) Pressure depends on the column of liquid above
and not on the cross section area.
Prepare different types of questions which suits this?

A hammer exerts a force of 1.5N …….
Given solution:
F = 1.5N
A1 = 2 x 10-6m2 A2 = 6 x 10-6m2
P1 = F / A1 = 1.5/2 x 10-6
=7.55Pa
P2 = F / A2 = 1.5/6 x 10-6
=2.55Pa
Prepare a question which suits this?

Find the thrust acting in SI …….
Given Solution
A = 300 x 10-4m2.
d = 1000 SI g = 10 N/kg Depth h = 0.06m
P = hdg = 0.06 x 1000 x 10 =600 Pa.
Thrust = P A
= 600 x 300 x 10-4
= 18 N
Preapre a question which suits this?

A simple U tube contains ….
hwater = 13.6 cm, R.D = 1
R.D(mercury) = 13.6
13.6cm x 1x g = hM x 13.6 x g
h = 1 cm.
Question please?

What should be the ratio of area
F1 = 0.5N
F2 = 15N A2 /A1= ?
F2 / F1 = A2 / A1
=0.5/15= 1:30
hydraulic machine – question
please?

the pressure of water on the ….
Given Pressure of liquid at firstfloor = 50000
Pressure at ground floor = 20000
Pg - Pf = height of first floor x d x g
30000 = h x 1000 x 10
h = 3m.
Question please?

In a hydraulic machine , a force
F1 = 2N A1 = 10cm2
F2 = ? A2 = 100 cm2.
F2 = F1 x A2 / A1
= 200/10 = 20 N
Hydraulic machine … question
please?

The areas of pistons in a
A1 = 5cm2 F2 =1250N A2 = 625 cm2.
F1 = ?
F1 = F2 x A1 / A2
= 1250 x 5/625
= 10 N
Question please?

The neck and bottom …
i) Fb = Fn x db
2 / dn
2
= 1.2 x 100 / 4
=30kgf
ii) Pascal’s law.

A force of 50kgf is applied …
Fs = 50 kgf ds = 5cm db = 25cm
Fb = ?
Fb = Fs x db
2/ ds
2.
= 50 x 625/25
= 1250kgf

A small ball of mass ‘m’ and density
ρ is dropped in a viscous liquid of
density ρ0 . After sometime the ball
falls with constant velocity.
Calculate the viscous force acting
on the ball.

Volume of ball V = m/ρ
Mass of liquid displaced by the ball,
m’ = (m/ρ) ρ0
When the ball move with constant
velocity,
Viscous force = effective wt.
= mg – m’g
= (m – m’) g
= mg ( 1- ρ/ ρ0 )

A dead body floats in water with its head
immersed in water. Why ?
Volume increases as the dead body
decays.
Become lighter than water and
floats up.
Head being heavy cannot displace
water more than its own weight.

Few Relative densities
• Petrol : 0.8 Ice : 0.92
• Sea water : 1.02 Glycerine : 1.26
• Glass : 2.5 Aluminium : 2.7
• Iron : 7.86 Copper : 8.92
• Silver : 10.5 Mercury : 13.6
• Gold : 19.3 Platinum : 21.5
• Osmium (highest on earth ) : 22.5

Density of mixture of liquids - 1
• Two liquids of densities ρ1 and ρ2, masses m1
and m2 mixed .
• Density of mixture
• ρ = (m1 + m2) / (V1 + V2)
= (m1 + m2) / [(m1 / ρ1) + (m2 / ρ2) ]
If m1 = m2, ρ = 2 ρ1 ρ2 / (ρ1 +ρ2 )

Density of mixture of liquids - 2
• Two liquids of densities ρ1 and ρ2, having
volumes V1 and V2 mixed
• Density of mixture
ρ = (m1 + m2 ) / (V1 + V2)
= (ρ1 V1 + ρ2 V2 ) / (V1 + V2)
If V1 = V2, ρ = ρ1 + ρ2 / 2

Effect of Temperature on Density
• Density decreases with increase in temperature
as volume increase and mass constant .
ρ α 1/ V
ρ’ / ρ = V / V’ = V / (V + dV )
= V / V + VγΔT
ρ’ = ρ / 1 + γΔT
How can you make oil sink in water ?

Name two substances , which are denser in
their liquid states than their solid state ?
Iron iodine

Activity : Put 4 naphthalene balls in soda water taken in
a tumbler.
• Observation : naphthalene balls dance
• Reason : CO2 gas bubbles stick with rough
surface of n-balls. Effective vol increases ,
upthrust increases.
• As the ball comes up bubbles grow ,and burst
and n- balls sink and continue the process or
dancing. Dr. Pius Augustine, S H College, Kochi

Archemedes 287 BC – 212 BC

Archemedes’ principle
A body wholly or partially
submerged in a fluid is buoyed up
by a force equal the weight of the
displaced fluid.

Law of Floatation
• Weight = upthrust.
• V D g = v ρl g
Fraction of volume immersed
v / V = D / ρl
% vol. immersed = (v / V) * 100
= (D / ρl ) * 100

R.D of a solid, liquid
 R.D of solid = Wt in air
loss of weight in water
 R.D of liquid = loss of wt in liquid
loss of wt. in water

Buoyant force in accelerating fluid
Body in a liquid in an elevator
FB = V ρL g eff
For a freely falling lift, g eff = 0
Eg : air bubbles will not rise up in free
fall.

A piece of ice is floating in a glass vessel filled
with water. How will the level of water in the
vessel change when the ice melts?
Ans: no change
• Wt. of ice piece = upthrust
• mg = V immersed ρwater g
• ie V immersed = m / ρwater
• Vwater formed on melting = m / ρwater

A piece of ice having a stone frozen in it floats in a glass
vessel filled with water. How will he level of water in the
vessel change when the ice melts ?
• Ans : level decrease.
• When stone floats volume of water displaced was more
than the volume of stone, so that upthrust became
sufficient to balance the wt of stone.
• After melting stone sinks. Volume displace is equal to
its own volume (less than before, hence level falls) not
sufficient to support the stone to make it float.

• Wt. of( ice + stone) = upthrust (mice +
mstone)g = V immersed ρwater g
• ie V immersed = mi / ρw + ms/ ρw
• Vwater formed on melting V1 = mice / ρwater
• Volume of water displaced due to sinking
stone V2 = ms / ρs
• Since ρs > ρw ,
V1 +V2 < V immersed ie. Level falls

Ice floats in water with about nine – tenths of its
volume submerged. What is the fraction submerged
for and iceberg floating on fresh water lake of a
(hypothetical) planet whose gravity is ten times that
of the earth ?
Same as that on earth. It is independent of
gravity.
Mass of floating body = mass of liquid displaced

A man sitting in a boat, which is floating in a pond. If
the man drinks some water from the pond, will the
level of water in the pond decrease ? Explain.
No. Wt of body = wt of water displaced
When he drinks water from the pond in which it is
floating, wt of the floating body increases in wt by
the amount of water missing from the pond.
To balance the wt of the floating body , same
amount of water should be displaced again. So
level remains same.

A boat floating in a water tank is carrying a
number of large stones. If the stones were
unloaded into water, what will happen to water
level ?
Water level will come down.
(Situation is same as ice with a stone
inside is melting).
Volume of water displaced by stone
when sinking is less than when it is
floating.

An ornament weighing 50g in air weighs only
46g in water. Assuming some copper is mixed
with gold to prepare the ornament .Find the
amount of copper in it. R.D = 20(Au) and 10
(Cu)
• Mcu = m, Mau = (50-m)
• V cu = m/10 and V au = (50-m) / 20
• Loss in wt = upthrust
• 4 gf = (V cu+ V au) x 1 gf
= [m/10 + (50-m) /20 ]
Ans: m = 30 g

centre of buoyancy
The centre of gravity of the displaced
liquid through which buoyant force is
acting vertically upward is called
centre of buoyancy.

Equilibrium of floating body
• Wt of the body and the buoyant
force must act on the same
vertical line.
ie : C.G and C.B should be on the
same vertical line.

Metacentre
• When the body is tilted, shape of the displaced
liquid changes.
• Centre of buoyancy shifts a little and may not be
in vertical line with centre of gravity of the body.
• Meta centre is that point on the central line
where the vertical line passing through the
centre of buoyancy cuts the central line.

Stable equilibrium
Heavily loaded at the bottom, G is lowered.
C.B is above C.G.
If tilted, M is above G.
Weight and buoyant force will form a
couple which brings back to original
position

Unstable equilibrium
• Heavily loaded at the top
C.B comes below C.G.
•If tilted, M lies below G.
• Couple formed turn the boat further
away from original.

Neutral Equilibrium
Floating body spherical in shape.
Tilt - no change in C.G or C.B
C.G always coincide with C.B.

Self test 1
When a cube of wood floats in water, 60%
of its volume is submerged. When the
same cube floats in an unknown fluid
85% of its volume is submerged. Find the
densities of wood and the unknown fluid.

Self test - 2
• A cubical block of ice floating in water
has to support a metal piece
weighting 0.5kg. What can be the
minimum edge of the block so that it
does not sink in water ? Specific
gravity of ice = 0.9

Self test - 3
• A bargain hunter purchases a ‘gold’
crown at a flea market . After she gets
home, she hangs it from a scale and finds
its weight in air to be 7.84 N. She the
weighs the crown while it is immersed in
water and now the scale reads 6.86N. Is
the crown made of pure gold.Dr. Pius Augustine, S H College, Kochi

Why can a liquid easily change its shape,
while a solid cannot?
Force of cohesion in
liquids is very small
compared to that in case
of solids

Why does melting point of ice increase with
decrease in pressure and vice versa ?
When higher pressure is applied on ice, it
tries to decrease the volume of ice
although its mass remains same. Hence,
it tries to increase the density of ice.
Since water density is higher than ice, high
pressure changes ice to water.

Why do glaciers melt at the bottom ?
Due to weight of upper layers
pressure increases hence density
of bottom most layer is maximum.
(towards water)

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision
Dr. Pius Augustine, SH College, Kochi

118
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
https://www.facebook.com/piustine
Please share
Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

16 pius augustine fluid pressure and flotation

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (20)

Semelhante a 16 pius augustine fluid pressure and flotation

Semelhante a 16 pius augustine fluid pressure and flotation (20)

Mais de PiusAugustine

Mais de PiusAugustine (20)

Último

Último (20)

16 pius augustine fluid pressure and flotation