Fluid Mechanics Chapter 13 2 Fluid Anything that can flow A liquid or a gas Physics Chapter 13.
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Transcript of Fluid Mechanics Chapter 13 2 Fluid Anything that can flow A liquid or a gas Physics Chapter 13.
Fluid MechanicsChapter 13
Physics Chapter 13 2
Fluid• Anything that can flow• A liquid or a gas
Physics Chapter 13 3
Density• Mass per unit volume
• Where r (rho) is the density, m is mass, and V is volume
• A homogeneous material has the same density throughout
• The SI unit of density is the kg/m3.
V
m
Physics Chapter 13 4
Specific gravity• Should be called relative density, but
we are stuck with the traditional term• The ratio of its density to the density
of water.
water
material
gravity specific
Physics Chapter 13 5
Pressure• Pressure is force per unit area,
expressed in Pascals (Pa). 1 Pa = 1 N/m2
A
Fp
Physics Chapter 13 6
Pressure changes• Pressure increases with depth
– Atmospheric pressure is greater at sea level than on top of a mountain
– Water pressure is greater in deeper water
• When y2 is greater, p2 is less.
1212 yygpp
Physics Chapter 13 7
Open containers• The pressure at the surface is
atmospheric pressure, or p0. If we are at a depth, h, below the surface,
ghpp
ghpp
0
0
Physics Chapter 13 8
Pascal’s Law• If we increase the pressure at the
surface, the pressure at any depth increases by the same amount.
• The pressure is transmitted throughout the fluid – if it has a uniform density – this is a fairly safe assumption for most liquids and for gases over small distances.
Physics Chapter 13 9
Pascal’s Law• Used in hydraulics to use a small
force over a small area to exert a large force over a large area.– See page 304
2
2
1
1
A
F
A
Fp
Physics Chapter 13 10
Gauge pressure• If the pressure in your tire equals
atmospheric pressure, the tire is flat.• When your pressure gauge reads
32 psi, that means the pressure in the tire is 32 psi above the atmospheric pressure.
Physics Chapter 13 11
Absolute pressure• Total pressure
• Atmospheric pressure at sea level is 101.3 kPa or 14.7 psi. Also called 1 atm
ga ppp 0
Physics Chapter 13 12
Example• A residential hot water heating
system has an expansion tank in the attic, 12 m above the boiler. If the tank is open to the atmosphere, what is the gauge pressure in the boiler? What is the absolute pressure?
• pg= 118 kPa, pa=219 kPa
Physics Chapter 13 13
Open-tube manometer
• Measures the pressure in a container.
gaugepghpp 0
Physics Chapter 13 14
Barometers• Long glass tubes full of mercury used
to measure atmospheric pressure.
h
ghp 0
ghpp 0
ghp 00
Physics Chapter 13 15
Buoyancy• When an object is less dense than
water, it floats.
Physics Chapter 13 16
Archimedes's principle• When an object is completely or
partially immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object.
• We call this upward force the buoyant force.
Physics Chapter 13 17
Weight of water displaced
V
m
Vm
mgw
gVw
Physics Chapter 13 18
Example• A cork has a density of 200 kg/m3.
Find the fraction of the volume of the cork that is submerged when the cork floats in water.
0, corkbuoyantynet wFF
0 corkwater ww
corkwater ww
Physics Chapter 13 19
Example continued
totalcorksumbergedwater gVgV
totalcorksumbergedwater VV
water
cork
total
sumberged
V
V
5
1
kg/m 1000
kg/m 2003
3
total
sumberged
V
V
Physics Chapter 13 20
Example• An ore sample weighs 14.00 N in air.
When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 9.00 N. Find the total volume and the density of the sample.
Physics Chapter 13 21
Example continued0 wFTF Bnet
TwFB
TwgVwater
g
TwV
water
Physics Chapter 13 22
Example continued
23 m/s 8.9kg/m 1000
N 00.9N 00.14 V
34 m 1010.5 V
Physics Chapter 13 23
Example continued
gVw
gV
w
342 m 1010.5m/s 8.9
N 00.14
3kg/m 1280
Physics Chapter 13 24
Fluid Flow• An ideal fluid is incompressible and
has no internal friction.• We will only deal with laminar flow,
which has a steady-state pattern.• We will not deal with turbulent flow,
which is chaotic.
Physics Chapter 13 25
Continuity equation• The mass of a moving fluid doesn’t
change as it flows.
tvAtvA 2211
2211 vAvA
Physics Chapter 13 26
Volume flow rate• The rate at which volume crosses a
section of the tube:
Avt
V
Physics Chapter 13 27
Example• Blood flows from an artery of radius
0.3 cm, where it’s speed is 10 cm/s into a region where the radius has been reduced to 0.2 cm. What is the speed of the blood in the narrower region?
• 22.5 cm/s
Physics Chapter 13 28
Bernoulli’s Equation• Relates pressure, flow speed, and
height for flow of ideal fluids.• Derived in book by applying the work
energy theorem to a flowing fluid
2222
2111 2
1
2
1vgypvgyp
Physics Chapter 13 29
Bernoulli’s Equation• Make sure that your units are
consistent.– Always use pascals, kg/m3, and m/s
• Always use either all absolute pressures or all gauge pressures.
Physics Chapter 13 30
Example• A large tank of
water has a small hole a distance h below the water surface. Find the speed of the water as it flows from the tank.
• Vb=sqrt(2gh)
Physics Chapter 13 31
On your own• Water enters a house through a
pipe with an inside diameter of 2.0 cm at an absolute pressure of 4.0 x 105 Pa. A 1.0 cm diameter pipe leads to the second-floor bathroom 5.0 m above. When the flow speed at the inlet pipe is 1.5 m/s, find the pressure and volume flow rate in the bathroom.
• 3.3 x 105 Pa 4.7 x 10-4 m3/s