Liquids & Buoyant Force

Notes (p275 HRW)

Liquids

Study of liquids

Hydrostatics liquids that are stationary Archimedes, Pascal

Hydrodynamics liquids that are moving Bernouilli

Fundamental Characteristic

Density ()

How is density defined? mass/volume

= m/V What are density units in SI

kg/m3 (standard) or gm/cc (common) Example

water = 1000 kg/m3 (or 1 gm/cc) gold = 19.3 x water lead = 11.3 x iron = 7.8 x ice = 0.92 x balsa = 0.12 x air = 1.2 kg/m3

Lower density floats

on higher density

Pressure (p)

Definition:

force perpendicular to plane/area over which force is acting P = Force/Area = F/A

SI Units = pascals (Newtons/meter2) Air Pressure

Standard air pressure @ sea level and 20C, expressed as: 1.01 x 105 Pa 1 atmosphere 760 mm (or 76 cm) of mercury 30 inches of mercury

Measured by a barometer or manometer Average tire pressure ~ 200 kPa or 30 psi (lbs/in2)

Hydrostatic (Gauge) Pressure

Fluid pressure increases with depth because the water at a depth must support the weight of water above it. Ex.

Diving to the bottom of the deep end of a pool what do you feel?

Air pressure P = gh, where

= density of fluid g = 9.8 m/sec2 h = depth of fluid (ex. height of water

column)

This is gauge pressure

Container shape?

NO EFFECT!

Absolute/Total Pressure

Add atmospheric pressure (Pair) which acts on the surface of the fluid and the total pressure becomes Ptotal = Pair + gh

Generically The pressure at the bottom of a

column (Pb) equals the pressure at the top (Pt) PLUS the pressure due to the column, or

Pb = Pt + gh

Practice - submarines

A sub dives to a depth of 200 m. How

much water pressure must the hull be

able to withstand, or what is the (gauge)

water pressure at 200 m?

Solve P = gh P = 1000 x 9.8 x 200 P = 1.96 x 106 Pa Every sq meter of surface must

withstand ~ 2 million newtons

Note: in this example we have NOT included the air pressure pushing on the top of the water!

Submarines

Maximum depth classified, but generally believed to be ~1500 ft for US

and ~2500 ft for Russian

Sub disasters

Thresher (63), sank off Cape Cod in 8400 ft after joint to outer hull failed, flooding sub

Kursk (2000), Barents Sea, 350 ft after torpedo accident

Practice

How deep (h) must a diver go before he experiences another atmosphere (1.01 x 105 Pa) of water pressure?

Solve for h in water ( = 1000 kg/m3) P = gh 1.01 x 105 = 1000 x 9.8 x h h = 10.31 m (~34 feet)

Roughly, every 30 feet of dive adds 1 atmosphere of pressure to a diver

Interesting facts on diving!

Deepest free dive

124 m (~400 ft) feet Deepest assisted dive

214 m (~700 ft) Breath holding record

>19 minutes

Mini-lab

Density determination of 3 samples

Measure Write-up Submit

Pascals Principle

Pressure applied to an enclosed fluid is

transmitted equally and undiminished to

every part of the fluid, as well as the walls

of the container.

P1 = P2, (Pressure a point 1 = pressure at point 2)

2

2

1

1

A

F

A

F

Application of Pascals Principle

Hydraulic lift service stations

Examples of Pascals Principle

Examples

Example

The small piston of a hydraulic lift has an

area of 0.2 m2. If a car weighing 1.2e4 N

sits on the large piston, area 0.9 m2, how

large a force must be applied to the small

piston to support the car?

F1/A1 = F2/A2 F1/0.2 = 1.2e4/0.9 F1 = 0.2*1.2e4/0.9 = 2.7e3 N

What is buoyancy?

In physics, buoyancy is

the upward force acting

on an object in a fluid,

and can be:

Positive Neutral Negative

Alligators & crocodiles?

What causes buoyancy?

Buoyancy is the result of the difference

in pressure exerted on the top and

bottom of an object.

Question

If you place a rock into a

bucket of water, say filled,

what will you observe about

the water line in the bucket?

It will rise to reflect the

volume of the rock if the rock was 0.1 m3, the water

would rise 0.1 m3, b/c the

rock is submerged.

This is an example of Archimedes Principle

Archimedes Principle - example

In air the stone

weighs 44 N

In water the stone

weighs 36 N

Buoyant force is the

difference = 8N

Buoyancy Example

Weight in

air Apparent

weight

Fb = Weight in air weight in water

Buoyancy - Archimedes

Archimedes Principle When a body is partly or wholly submerged in a fluid,

it will experience a buoyant force (Fb)equal to the weight of the fluid displaced.

Buoyant (Upthrust) force (Fb) Fb = Weightfluid displaced = (massfluid)*(g) Fb = (fluid)*(Vfluid displaced)*(g) (Note: =m/V or m= *V)

Fb = (V)*g directed upward! Case 1 object is submerged

Fb = (fluid)*(Vfluid displaced)*(g) Case 2 object is partially submerged (floating)

Fb = (object)*(Vobject)*(g)

Buoyancy Summary Table

IF THEN

object > fluid Wobj > Fb sinking

object = fluid Wobj = Fb neither sink nor float

object < fluid Wobj < Fb float

= density, W = weight Fb = buoyant force

Example of Archimedes

Principle & Buoyant Force

If a house brick of density () 2000 kg/m3 and volume (V) of 0.00123 m3 is placed in

a bucket of water, what is the buoyant force

(Fb) acting on a brick?

Solve: Fb = Vg

Fb = 1000 x 0.00123 x 9.8

Fb = 12.05 N

Buoyant Force Practice

An ice cube is floating in a glass of water

(=1000 kg/m3). The ice, whose density is 917 kg/m3, has dimensions of 0.03 x 0.02 x

0.02 m. What is the buoyant force on the ice?

Solve: Note: the ice is floating thus the

buoyant force = weight of the ice

Fb = (V)*g (use , V for ice, not water) Fb = 917*(0.03*0.02*0.02)*9.8 Fb = 0.11 N

Buoyant Force Practice

A ferry boat is 4 m wide and 6 m long. When a truck pulls onto it, the boat sinks 4 cm in the water. What is the weight of the truck?

Use Archimedes Principle: Weight of truck = weight of water displaced (find

this displacement)

Weight = mass x g Mass of water (m) = density x volume m= 1000 x (4 x 6 x 0.04) = 960 kg

Weight = m x g = 960 x 9.8 = 9,408N

Buoyant Force Practice

Example

A piece of metal weighs 7.84N in air and 6.86N when completely immersed in water.

What is the buoyant force? Fb = 7.84 6.86 = 0.98N

What is the density () of the object? Fb = Vg (, V refer to the fluid when submerged) V = Fb /g = 0.98/(1000*9.8) = 0.0001 m3 Mass = Weight/9.8 = 0.8 kg = m/V = 0.8/0.0001 = 8000 kg/m3

Buoyancy - icebergs

If an object is floating on the

surface, then the volume that

is below the surface can be

determined as follows:

Vf/Vo = o/f, where Vf= volume of object that is below

surface

Vo= volume of the object o = density of the object f = density of the fluid

% Iceberg in salt water that is below surface = .92/1.025 = 89%