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Ch. 15 Fluids. Fluids. Substances that flow readily, usually from high pressure to low pressure. They take the shape of the container rather than retain their shape. We refer both liquids and gases as fluids. Density. Is the mass of a substance divided by the volume of that substance.

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Ch. 15 Fluids


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fluids
Fluids
  • Substances that flow readily, usually from high pressure to low pressure.
  • They take the shape of the container rather than retain their shape.
  • We refer both liquids and gases as fluids.
density
Density
  • Is the mass of a substance divided by the volume of that substance.
density equation
Density Equation

Mass

Density =

Volume

slide5

m

D

V

density units
Density Units
  • Metric: kg / m3

or g / cm3

  • English: lbm / ft3
slide7
Sample Problem: What is the volume of my 2.16 g titanium wedding band if the density is 4.50g/ cm3?
slide8
G: m = 2.16 g,

D = 4.50 g/cm3

U: V = ?

E: D = m / V  V = m/D

S: V = 2.16 / 4.50 g/cm3

S: V = 0.48 cm3

pressure
Pressure
  • is defined as force per unit of area.
equation
Equation

Force

Pressure =

Area

slide12

F

A

P

units of pressure
Units of Pressure
  • English: lb / ft2, lb / in2, or p.s.i.
  • Metric: N/m2 or Pascal (Pa)
slide14
Sample Problem: If an airplane window that is 40 cm by 60 cm feels a pressure of 40,000 Pa. How much force is acting on the window?
slide15
G: L = 40 cm = 0.4 m

w = 60 cm = 0.6 m

P = 40,000 Pa

U: F = ?

E: F = PA

slide16
We don’t have area (A),

A = Lw

A = (.4)(.6)

A = 0.24 m2

atmospheric pressure
Atmospheric Pressure

The pressure of the earth’s atmosphere pushing down on you.

slide20
Earth's atmosphere is pressing against each square inch of you with a force of 1 kilogram per square centimeter (14.7 pounds per square inch).
slide22

Sample ProblemCalculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

slide26

Since pressure acts equally in all directions, gauge pressure is used to deal with this.

  • If you have a flat tire, is there a pressure in the tire or is the pressure zero?
  • Yes, it is equal to atmospheric pressure.
gauge pressure p g
Gauge Pressure (Pg)
  • Is the pressure inside an inflated object, that is above the atmospheric pressure.
  • Pg = P – Patm
  • If a tire is inflated to 35 psi, that means it is 35 psi above the atmospheric pressure. So the pressure inside the tire is actually 35 psi + 14.7 psi.
pressure increases with depth
Pressure increases with depth.

The deeper the body of water or you go, the more water there is on top of you per square inch.

pressure depth relationship
Pressure depth relationship

Phyd = rgh

r – weight density of liquid

slide31
The pressure of a liquid is the same at any given depth regardless the shape of the container.
absolute pressure
Absolute Pressure
  • Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure.
  • pabs = patm + rgh
  • p2 = p1 + rgh
pascal s principle
Pascal’s Principle

Pressure applied to a fluid in a closed container is transmitted equally

slide39
By the definition of Pressure:

F1/A1 = F2/A2

So if the 2nd area is increased by a factor of 25.

slide44
Sample problem: The small piston on a hydraulic lift has an area of 0.20 m2. A car weighing 1.2 x 104 N sits on the rack with a large piston. If the area of the large piston is 0.9 m2, how much force must be applied to the small piston to support the car?
slide45
G: A1 = 0.2 m2, F2 = 1.2 x 104 N, A2 =0.9 m2

U: F1 = ?

E: F1/A1 = F2/A2

F1 = F2A1/A2

slide48
The distance the 2nd piston moves is equal to the reciprocal of the factor of the ↑ or ↓ in area times the distance the 1st piston moves.
buoyancy
Buoyancy
  • The apparent loss of weight of an object that is submerged in a fluid.
buoyant force
Buoyant Force

Is the upward force equal to the weight of the fluid displaced.

slide53
Buoyant force is due to pressure difference between top and bottom of object.
  • Pressure difference does not depend on depth
slide62
If denser than the fluid, it sinks.
  • If less dense than the fluid, it will float.
  • If the same density, it will neither float nor sink.
archimedes principles
Archimedes Principles

The buoyant force is equal to the weightof the liquid displaced. Immersion:  all or part under water.Submersion:  completely under water

slide67

Vsub – submerged volume

Vs – volume of the solid

rs – density of solid

rf – density of fluid

slide68

Sample problem: Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats? (density of water is 1000 kg/m3)

principle of floatation
Principle of Floatation
  • A floating object will displace a weight of fluid equals to its own weight.
specific gravity
Specific Gravity

Is the ratio of any substance’s density to the density of water.

slide72
Density of

Specific a substance

Gravity =

Density of

water

fluid flow continuity
Fluid Flow Continuity
  • The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe.
  • We can say this because liquids are not compressible, so mass conservation is also volume conservation for a liquid.
volume of a fluid moving past a point can be calculated by
Volume of a fluid moving past a point can be calculated by:

V = Avt

V: volume of fluid (m3)

A: cross sectional areas at a point in the pipe (m2)

v: speed of fluid flow at a point in the pipe (m/s)

t: time (s)

equation for continuity
Equation for Continuity

r1A1v1 = r2A2v2

  • r1, r2: weight density of fluids at point 1 and 2
  • A1, A2: cross sectional areas at points 1 and 2
  • v1, v2: speed of fluid flow at points 1 and 2

Use for gases.

for an incompressible fluid a liquid
For an incompressible fluid (A liquid)

A1v1 = A2v2

  • A1, A2: cross sectional areas at points 1 and 2
  • v1, v2: speed of fluid flow at points 1 and 2
slide78

Sample problem: A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm? How much water per second flows through the pipe?

slide79

Sample problem: The water in a canal flows 0.10 m/s where the canal is 12 meters deep and 10 meters across. If the depth of the canal is reduced to 1.5 meters at an area where the canal narrows to 5.0 meters, how fast will the water be moving through this narrower region?

bernoulli s principle
Bernoulli’s Principle

The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow.

bernoulli s principle1
Bernoulli’s Principle
  • The pressure in a fluid decreases as the speed of the fluid increases.
bernoulli s theorem
Bernoulli’s Theorem
  • p + r g h + ½ rv2 = Constant
  • p : pressure (Pa)
  • r : density of fluid (kg/m3)
  • g: gravitational acceleration constant (9.8 m/s2)
  • h: height above lowest point (m)
  • v: speed of fluid flow at a point in the pipe (m/s)
slide85
fluid flows smoothly
  • fluid flows without any swirls
  • fluid flows everywhere through the pipe
slide86
fluid has the same density everywhere (it is "incompressible" like water)
slide90

Sample Problem: Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hose, the water flows out of a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle? If the pressure in the hose is 350 kPa, what is the pressure in the nozzle?

torricelli s law
Torricelli’s Law
  • Deals with the speed of a fluid as it flows through a hole in a container.

P1 + r g h1 + ½ rv12 = P2 + r g h2 + ½ rv22

Patm + r g h1 + 0 = Patm + 0 + ½ rv22

  • g h1 = ½ rv22
slide93

Sample Problem: An above-ground swimming pool has a hole of radius 0.10 cm in the side 2.0 meters below the surface of the water. How fast is the water flowing out of the hole? How much water flows out each second?