Pressure & Buoyancy

Foundation PhysicsFoundation Physics

Eye dropper filled with liquidsEye dropper filled with liquids

Maximum height which can be achieved by

ki isucking water in to a tube 10.3 m.How do we get thisHow do we get this value?

BarometerBarometer

vacuum

p0

Evangelista Torricelli1608 1647

760 mmHg= 760 torr 760mm

1608 - 1647

Hg

760 torr= 1013 hPa

Hg

The atmospheric pressure is till today often reported in torr 1 torr = 133 Pa whereas 1 torr correspondsThe atmospheric pressure is till today often reported in torr. 1 torr = 133 Pa, whereas 1 torr corresponds to 1 mmHg. The standard atmospheric pressure is 760 mm Hg = 760 torr = 1013 mbar = 101’325 Pa = 1013 hPa. This is a typical atmospheric pressure. Generally the air pressure is influenced by the weather and the altitude. The unit torr was named after Evangelista Torricelli who discovered that the height of the mercury in glass tubes closed at one end is equal When the mercury declines from the upper part of themercury in glass tubes closed at one end is equal. When the mercury declines from the upper part of the tube it leaves behind a space without air. Torricelli therefore postulated the vacuum, which could not exist according to Aristotle’s then believed doctrine.

Measurement of pressure based on Pascals principle

liquid

air

q

Common blood measurement Spinal column pressure measurementCommon blood measurement

Pressure is transmitted undiminishedMaximum Blood pressure: systolic pressure

measurement

Minimum Blood pressure: diastolic pressureImportant place the cuff at the height of the heart

Pressure Distribution in HumansPressure Distribution in Humans

While lying the pressure distribution in the big arteries is relatively homogeneous (ca. 100 torr = 133 mbar). Standing, the pressure distribution is inhomogeneous because of the pressure due to the weightdue to the weight.In a study of 100 subjects with no known history of hypertension, an average systolic blood pressure of 112.4 mm Hg and an average diastolic pressure of about 64.0 mm Hg was found

Pressure sensing elementPressure sensing element

Th i l t i l dThe pressure sensing element is a closed coiled tube connected to the chamber or pipe in which pressure is to be sensed. As the gauge pressure increases the tube will tend to uncoil, while a reduced gauge pressure will cause the tube to coil more tightly. This motion is transferred through a linkage to a gear train connected to an indicating needle.indicating needle.

Pressure gauges and fluidics applicationsg g pp

Bead placementBead placement on Pipette and in 1st trap

Bead in 3Dmovable trap

Bead in theBead in thedouble-trap

automatic

ivacuum-pressure

Bead held by suction syringe

Expansion bottles

3 m

by suction onmovable pipette

automatic valves

p pette

QuestionsQuestionsvacuum

p0

760 mmHg= 760 torr= 1013 hPa

760mm

Hg

Spinal column pressureSpinal column pressure measurement

Why can’t an absolute Why is mercury rather than water used ypressure in a gas be less than zero?

in barometers and in blood pressure measurements? If a manometer is used to measure spinal column pressure, why i it f bl t li l tiis it preferable to use saline solution rather than mercury?

BuoyancyBuoyancyBuoyancy arises from the fact that fluid pressure increasesBuoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is ( p p )an unbalanced upward force on the bottom of a submerged object.

Volume of water in equilibrium: Identical volume of other substancebuoyant force = weight force -> Identical buoyant force

-> can be measured by weight of watervolume

•The buoyant force is equal to the weight of the fluid displacedThe buoyant force is equal to the weight of the fluid displaced•The fraction of the object that is submerged is equal to the ratio of the density of the object to the density of the fluid

BuoyancyBuoyancyIn a liquid an object experiences a Fb

buoyant force Fb through the submerged volume V.

VFExplanation:

gVF Fb 1Explanation:We look at a submerged coboid. The forces due to the weight to the side faces cancel out each other The difference ofcancel out each other. The difference of the forces to the base and the top surface area ( ) are responsible for the b

12 FF l w

buoyancy.

Fb = F2 – F1= l .w .F1

.g(h + a) - l .w .F1 . g .h

= l .w .F1. g .a = F1

. g .V

BuoyancyBuoyancy

Buoyancy in terms of density:Density of object < density of water -> floats‘since object adds less mass to the same volume’‘since object adds less mass to the same volume’Density object > density of water -> sinks‘since object places more mass in same volume’since object places more mass in same volume

Question:Why does a person not float in air ?Displaced volume: 0.08m3

Mass of displaced volume: m = V = 1 25kg/m3Mass of displaced volume: m = .V = 1.25kg/m3

0.08m3 = 0.1kg-> Upward force (weight force) : F = m.g = 0.981 N Upward force (weight force) : F m g 0.981 N-> Typical weight (m=80kg): F = 784.8N

Ice and WaterIce and Water

• Why does ice float?• Why does ice float? Solids are generally denser than

liquidsliquids Liquids are generally less dense than

solidssolids• Ice should sink

I f t “ ll ” ld t i d th i (I• In fact, “really” cold water is denser than ice (I.e. water at 2oC is denser than ice at 0oC)

• If this wasn’t true, oceans and lakes would freeze from the bottom up

HydrometerHydrometer

What is the density of the person?mperson=80kgmsubmerged=2kg

A hygrometer floating in a fluid of density

msubmerged 2kg

Cross section of a ship. The average density of a fluid of density

0.87g/cm3. The greater the density the higher the hygrometer will float.

The average density of the ship is les than that of water.

Flowing liquidFlowing liquid

Equation of ContinuityEquation of Continuity• The flow of a liquid is constant throughout a system (if no

liquid is added or subtracted)liquid is added or subtracted)• The amount of water going into a pipe is the same as

coming outcoming out• Amount of liquid flow is:

Flow = A vFlow = .A.v

Flow: Poiseuille’s lawFlow: Poiseuille s law

tVF

21 PPF

Flow rate is defined as the 8 L

RF

o ate s de ed as evolume flowing per unit time.The quantitative relationship 4

8rLR

between flow rate and pressure is given in the middle equation to the right where R is the resistance to

r

(eta) = viscosityright, where R is the resistance to flow.

(eta) = viscosity

Flow rate in tubesFlow rate in tubes RPPF /21 RPPF /21

21

4

421 rLPPF

4

21 rLPPF

Lets double the tube length and see what happens to the flow rate:

1

LLF22

LLF

Next LectureNext Lecture

• To Be Covered: Fluids and Flow• To Be Covered: Fluids and Flow

• Reading: Chapter 6 Section 6 5; 6 6 Section 6.5; 6.6