PHYSICS 231
Lecture 22: Pressure
Remco Zegers
Walk-in hour: Thursday 11:30-13:30 am
Helproom
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Solids:
Previously
FL0
F/A
Young’s modulus
Y

L / L0 AL
F/A
Fh
Shear modulus
S

x / h Ax
F / A
P
Bulk modulus
B

V / V0
V / V0 Also fluids
P  pressure
General:
P=F/A (N/m2=Pa)
=M/V (kg/m3)
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Force and pressure
Air (P=1.0E+5 Pa) A
P=0
Vacuum
F
What is the force needed to move the lit?
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Magdeburg’s hemispheres
Otto von Guericke (Mayor of Magdeburg, 17th century)
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Pressure vs Depth
Horizontal direction:
P1=F1/A P2=F2/A
F1=F2 (no net force)
So, P1=P2
Vertical direction:
Ftop=PatmA
Fbottom=PbottomA-Mg=PbottomA-gAh
Since the column of water is not moving:
Ftop-Fbottom=0
PatmA=PbottomA-gAh
Pbottom=Patm+ gh
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Pressure and Depth:
Pdepth=h =Pdepth=0+ gh
Where:
Pdepth=h: the pressure at depth h
Pdepth=0: the pressure at depth 0
=density of the liquid
g=9.81 m/s2
h=depth
Pdepth=0=Patmospheric=1.013x105 Pa = 1 atm =760 Torr
Pascal’s principle: If P0 changes then the pressures
at all depths changes with the same value.
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A submarine
A submarine is built in such a way that it can stand pressures
of up to 3x106 Pa (approx 30 times the atmospheric
pressure). How deep can it go?
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Does the shape of the container matter?
NO!!
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Your homemade pressure difference meter
(PART I)
h1
Pdepth=h =Pdepth=0+ gh
Part 2 on Friday!
h2
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Pascal’s principle
In other words then before: a change in pressure applied
to a fluid that is enclosed in transmitted to the whole
fluid and all the walls of the container that hold the fluid.
P=F1/A1=F2/A2
If A2>>A1 then
F2>>F1.
So, if we apply a small
force F1, we can exert
a very large Force F2.
Hydraulic press demo
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Hydraulic brake
What is the frictional
torque about the axle
exerted by the shoe
on the wheel drum when
a force of 44N is applied
to the pedal?
F=44N
6.4cm2
1.8 cm2
R=0.34 m
coef of
friction: 0.5
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Pressure measurement.
The open-tube manometer.
The pressure at A and B is
the same:
P=P0+gh
so h=(P-P0)/(g)
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Pressure Measurement: the mercury
barometer
P0= mercurygh
mercury=13.6E+03 kg/m3
mercury,specific=13.6
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Pressure at different altitudes
The pressure in the lecture room equals 1 atm
(1.013E+05 Pa). What will the pressure on the 6th floor
of the BPS building be (h=20m)? And at the top of
mount Everest (h=8500 m)?
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