Fluids
TableofContents
·Density
·Specific Gravity
·Pressure in Fluids
·Atmospheric Pressure and Gauge Pressure
·Pascal's Principal
·Buoyancy and Archimedes'Principle
·Fluids in Motion & Bernoulli's Principle
·Torricelli's Theorem
Density
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Density
You may recall that the four common phases, or states, ofmatter that are observable in everyday life are solid, liquid, gas, andplasma. (There are actually many more but they are not common.) Solids maintain a fixed volume and shape, liquids maintain a fixed volume but not shape, and gases can change both. Plasma is an ionized state of matter similar to gas. Since gasses and liquids both flow, they are collectively called fluids.
Density
What weights more a pound of feathers or a pound of bricks? This is a silly questions since they are both a pound.
Sometimes people say that iron is "heavier" than wood.But if you have a log of wood it would be heavier than one smalliron nail.
What we should really say is that iron is more dense than wood.
Density
The density of an object is its mass per unit volume:
ρ(rho)is density.m is mass.
V is volume.
The SI unit for densityis kg/m3but sometimes itismeasured in g/cm3.To convertfrom g/cm3tokg/m3multiplyby1000.
1The density of a substance is, its mass is m and its volume is
V.If the volume is tripled, what is the new mass?
Am/3
B3m
Cm
Dm/6
E6m
2. Liquid A has twice the density of liquid B.A certain experiment needs samples of A and B that have the same mass. What needs to be true about their volumes?
AVA=VBB2VA=VBCVA=2VB
DVA/2=VBEVA=4VB
3 What is the density(in kg/m3) ofan object that hasamass of 2kg andavolume of4m3?
Slide 10 (Answer) / 71
Slide 11 / 71
4A container of water has a mass of 5kg.What is the volume of thiscontainer(inm3)? Thedensityof water is1000kg/m3. (Neglect the mass of the container.)
SpecificGravity
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SpecificGravity
The specific gravity of a substance is the ratio of its density to the density of water.
The densityofwaterat4oCis1g/cm3or 1000kg/m3.
SpecificGravity
Specific gravity is a ratio so it has no units.
A substance with a specific gravity less than one means that it is less dense than water and will float on water and a substance with a specific gravity greater than one means that it is more dense than water and will sink in water.
5The following are specific gravities of various objects.Which would float on water? Select two answers.
Copper - 8.96
Balsa - 0.20
Aluminum - 2.70
Oak - 0.78
[Thisobjectisapulltab]
6What is the specific gravity of a substance whose density is 450kg/m3?
7Mercury's specific gravity is about 13.5.What is its density inkg/m3?
PressureinFluids
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PressureinFluids
Pressure is defined at the force per unit area.
Pressure is a scalar and its units are in Pascals. 1Pa=N/m2.
This definition of pressure is true in any situation, not just fluids. You can see from the equation that pressure if related to force and area. Think about what it would mean to get your foot stepped on by a sneaker or a high heal. Which would hurt more? Why?
PressureinFluids
Fluids can exert a pressure normal to any contact surface.
Pressure is the same in everydirection in a fluid at a given depth.If it were not, the fluidwould flow.
8A perpendicular force is applied to a certain area and produces apressure P. If the same force is applied to half the area, the new pressure on the surface is:
A2P
B4P
CP
DP/2
EP/4
9A 50kg person stands on a square board with sides of 2m.Whatis the pressure (in Pa) exerted on the ground by the board?
10Four cubes lie on a table top as shown below, which two exertthe same pressure on the table? Select two answers.
ρ =4g/cm3ρ = 1 g/cm
ρ =2g/cm3
ρ =6g/cm3
s = 2 cm
s = 3cm
s = 5cm
s = 6cm
ABCD
PressureinFluids
The pressure at a depth of h below the
surface of the fluid is due to the weight (mg) of the fluid above it.
Multiply top and bottom by h.
V = Ah
#=m/V
PressureinFluids
PPP
The pressure at a given point depends on only the density of the fluid and the depth. (Not the shape of the
container.)
This is valid for liquids whose density does not change with depth.
11There are five containers of the same fluid in a physics lab. Which has the greatest pressure at the bottom of the container?
ABCDE
12What is the pressure (in Pa) at the bottom of a swimming pool whose depth is 2m?
AtmosphericPressureand GaugePressure
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AtmosphericPressureandGaugePressure
Atsealevel,theatmosphericpressureisabou1t.013x105Pa.Thisiscalled1atm.
Anotherunitofpressureisthebar.
1bar=1.00x105Pa.
Mostpressuregaugesmeasurethepressure
aboveorbelowatmosphericpressure.Thisiscalledgaugepressure.
Absolutepressureisatmosphericpressureplusgaugepressure.
AtmosphericPressureandGaugePressure
Torricelli invented amercury barometerto measure atmosphericpressure.
Sometimes airpressure is described inmillimeters or inches of mercury.
A glass tube is filled with mercury. This glass tube sits upside down in a container, called the reservoir, which also contains mercury. The mercury level in the glass tube falls, creating a
vacuum at the top.
P = 0
h
P=1atm
AtmosphericPressureandGaugePressure
The barometer works by balancing the pressure of mercury in the glass tube against the atmospheric pressure. If the pressure of mercury is less than the atmospheric pressure, the mercury level in the glass tube rises. If the pressure of mercury is more than the atmospheric pressure, the mercury level falls.
Atmospheric pressure is basically the pressure of air in the atmosphere above the reservoir, so the level of mercury continues to change until the pressure of mercury in the glass tube is exactly equal to the pressure of air above the reservoir.
P=0
h
P = 1 atm
13A diver in the ocean measures guage pressure to be 515kPa. What is the absolute pressure?
A 101kPa B 313kPa C 515kPa D 616kPa E 5150kPa
14What is the absolutepressure (in Pa) at the bottomof aswimming pool whose depth is 2m?
Pascal'sPrincipal
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Pascal's Principle
Pascal's principle states that if an external pressure is applied to a confined and incompressible fluid, thepressureeverywhere in the fluid increases by that amount.
Pascal's Barrel is an experiment attributed to Pascal but it is unclear if it was ever preformed by him. In this experiment, a 10 meter long tube was inserted into a barrel filled with water. When water was poured into the tube, the increase in pressure caused the barrel to burst.
Pascal's Principle
Fin
Fout
15In a hydraulic lift, the large piston has five times the area as the small piston. How much extra force can the large piston exert?
AOne tenth as much as the small piston BOne fifth as much as the small piston C The same as the small piston
DFive times as much at the small piston EFifty times as much as the small piston
16The small piston of ahydraulic lift has an area of10cm2and its large piston has anarea of 100 cm2.A40 N forceis applied to the small piston. What is the weight of the load can belifted by the large piston?
17The small piston of a hydraulic lift has an radius of 15cmand its large piston has an radius of 30 cm. A 50 N force is appliedto the small piston. What is the mass of an object that can belifted by the large piston?
Buoyancyand Archimedes' Principle
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Buoyancy and Archimedes'Principle
The upward buoyant force on an object immersed in a fluid, partiallyor completely, is equal to the weight of the displaced fluid.
FB
FB
mg
FB
mg
mg
Buoyancy and Archimedes'Principle
If an object is submerged in a fluid, there is a net force onthe object because the pressure is greater at the bottom than at the topof the object. The buoyant force is upwardbecause the force is greater at bottom than at the top of the object.
F1
h1
h2
F2
Buoyancy and Archimedes'Principle
FB
mg
Where:
#Fis thedensity ofthe fluid.
mFis themass of thedisplaced fluid.V is the volume of the displaced fluid.
Buoyancy and Archimedes'Principle
The net force on a object is the difference between the buoyant force and the gravitational force.
Fscale
FscaleFB
mgmg
18Three objects of the same volume but different materials are completely submerged in water. They are zinc with a density of 7000 kg/m3, nickelwith adensity of8900 kg/m3, andsilver withadensity of 10500 kg/m3.Which has thegreatest buoyant force exerted on it?
AZinc
BNickel CSilver
DThey all have the same buoyant force.
EIt is impossible to tell without knowing the volume.
19A metal sphere weights 5N in air and 3N when it is submergedin water. What is the buoyant force on the sphere when it is submerged in water?
A0.2N B2N
C3N
D5N
E8N
20A metal sphere weights 5N in air and 3N when it is submergedin water. What is the buoyant force on the sphere when it is submerged in water?
A0.2N B2N
C3N
D5N
21An objecthas a volume of 2.0m3. What is thebuoyantforce on the object when it is completelysubmerged into water (density 1000kg/m3)?
22An object is submerged in water and attached to a rope asshown. If the specific gravity ofthe object is 0.8 and itsvolume is0.02m3what is the tension in Newtons in the rope?
Buoyancy and Archimedes'Principle
FB=mfluidg
Any floating object displaces its own weight of fluid.
mboatg
Buoyancy and Archimedes'Principle
For an object whose density is less than that of thefluid, there will an net force upward and it will rise until it is partial out ofthe fluid.
For a floating object, the fraction that is submerged isgiven by the ratio of the objects density to that of the fluid.
23A 1500 N object floats in water. What is the weight odfisplaced water?
24 A small empty row boat with a mass of 48kg floats on water. What is the volume of the water it displaces?
25 An object floats on water with 3/4 of it submerged.Whatis its specific gravity?
FluidsinMotion& Bernoulli'sPrinciple
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Fluids in Motion & Bernoulli's Principle
If the flow of a fluid is smooth, it is called streamlineor laminar flow.This is what we will deal with.
The mass flow rate is the mass that passes a givenpoint per unit time.The flow rates of a fluid must beequal, as long as no fluid is added or taken away.
This gives us the equation of continuity:
If the density of the fluid doesn't change, it can besimplified to:
Fluids in Motion & Bernoulli's Principle
Density does not typically change in liquids.Thismeans that where a pipe is wider the flow is slower.
v1v2A2
1
Fluids in Motion & Bernoulli's Principle
You can see this happening in a river when the water flow is slow when it is wide and fast when it is narrow.
26Water flows at a constant speed though one section of apipe, when it enters another section that is half the cross sectionalarea what happens to the speed of the water?
AThe speed is reduced to one fourth the original. BThe speed is reduced to one half the original.
CThe speed says the same. DThe speed is doubled.
EThe speed is quadrupled.
27Water flows through apipe of cross-sectional area10 cm2at arate of 15 m/s. The cross-sectional areaof the pipe isdecreased to 5cm2. What isthe waterrate inthe narrow section of the pipe?
28Water flows through two pipes that connect into one larger
pipe.The speed in the two pipes is 10 m/s and they eachhave a radius of 5 cm. The larger pipe has a radius of 15 cm. What is the speed of the water in the large pipe?
Fluids in Motion & Bernoulli's Principle
A fluid can also change height.If we look at thework done...
constant
v2A2
v1
A1
h2
h1
Fluids in Motion & Bernoulli's Principle
One thing this tells us is that as the speed of the water flow goes up, the pressure goes down.
constant
29A pipe has three different sections with three differentcross- sectional area. Where is the pressure the least?
AP1
BP2
CP3
DThe pressure is the same in all three sections. EThe pressures cannot be determined.
30Water flows through a horizontal pipe at a speed of10 m/s and pressure 2.5 x 105Pa.The pipe narrowsandthe water speed goes up to a 20 m/s. What is thepressure in the narrow sectionofthe pipe?
Slide 64 (Answer) / 71
Slide 65 / 71
31Water flows through a horizontalpipe of area 2 m2ata speed of 10 m/s andpressure 4.5 x105Pa. Thepipe narrows to1 m2 and goes to a height of 20 m. What is thepressure in the narrow section of the pipe?
v2A2
v1h
1
Slide 65 (Answer) / 71
Torricelli'sTheorem
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Torricelli's Theorem
v2=0
y2-y1
We can use Bernoulli's Principle,to find the speed of a fluidcoming out to spigot of an opentank. This is called Torricelli'sTheorem.
v1
32A container of water has spigot at its bottom.What happens to the water speed out of the spigot as the container empties?
AThe water speed decreases. BThe water speed increases.
CThe water speed stays the same.
33A container holds water at a depth of 5 m. There is aholein the
bottom of the container. At what speed wilwl hole?
ater flow outof the
Summary
DensityBuoyant Force
Specific Gravity
Equation of Continuity
Pressure
Bernoulli's Principle
Pressure in Fluids
constant