1. PHYSICS 231 Lecture 22: Pressure
Remco Zegers
Walk-in hour: Thursday 11:30-13:30 am
Helproom
PHY 231

2. Previously Young’s modulus Solids: Shear modulus Bulk modulus
Also fluids
General:
P=F/A (N/m2=Pa)
=M/V (kg/m3)
PHY 231

3. Force and pressure Air (P=1.0E+5 Pa) P=0 A Vacuum F
What is the force needed to move the lit?
Force due to pressure difference: Fpressure=PA
If A=0.01 m2 (about 10 by 10 cm) then
a force F=(1.0E+5)*0.01=1000N is needed to pull
the lit.
PHY 231

4. Magdeburg’s hemispheres
Otto von Guericke (Mayor of Magdeburg, 17th century)
PHY 231

5. 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
PHY 231

6. Pdepth=h =Pdepth=0+ gh
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.
PHY 231

7. 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?
Pdepth=h =Pdepth=0+ gh
3E+06=(1.0E+05)+(1.0E+03)(9.81)h
h=296 m.
PHY 231

8. Does the shape of the container matter?
NO!!
PHY 231

9. Your homemade pressure difference meter (PART I)
Pdepth=h =Pdepth=0+ gh h1
Part 2 on Friday! h2
PHY 231

10. 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
PHY 231

11. =F*R=6.2*0.34=2.1 NM Hydraulic brake FMC/AMC=FBC/ABC
FBC=44*1.8/6.4=12.4 N
Fshoe-drum=Fdrum-shoe=normal force
Ffriction=N=0.5*12.4=6.2N
=F*R=6.2*0.34=2.1 NM n F
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
PHY 231

12. Pressure measurement. The open-tube manometer.
The pressure at A and B is
the same:
P=P0+gh
so h=(P-P0)/(g)
If the pressure P=1.01 atm, what
is h? (the liquid is water)
h=(1.01-1)*(1.0E+05)/(1.0E+03*9.81)=
=0.1 m
PHY 231

13. Pressure Measurement: the mercury barometer
P0= mercurygh
mercury=13.6E+03 kg/m3
mercury,specific=13.6
PHY 231

14. 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)?
Just like the case for a fluid, the pressure changes
with depth (height in the case of air).
Plecture room=P6th floor+ airgh
P6th floor=Plecture room-airgh=1.013E *9.81*20=
= Pa ( 3 promille change)
Pmount everest=1.013E *9.81*8500=-6.3E+03 Pa????
The density of air changes with altitude, and so the
equation does not hold; it is very easy to compress air
(small bulk modulus) compared to e.g. water.
(see also next chapter)
PHY 231