Lecture 21
Goals:
• Chapter 15, fluids
• Assignment
 HW-8 due Tuesday, Nov 15
 Wednesday: Read through Chapter 16
Physics 207: Lecture 21, Pg 1
Fluids
 Another parameter
 Pressure (force per unit area)
P=F/A
SI unit for pressure is 1 Pascal = 1 N/m2
 The atmospheric pressure at sea-level is
1 atm = 1.013 x105 Pa
= 1013 mbar
= 760 Torr
= 14.7 lb/ in2 (=PSI)
Physics 207: Lecture 21, Pg 2
Incompressible fluids (liquids)
 What is the pressure at the bottom of the
container?
F=Mg=ρVg
F=ρAyg
Pressure=F/A=ρyg
y
P=ρgy
Area=A
Physics 207: Lecture 21, Pg 3
What if there is outside gas?
Pressure=P0
F=P0A+Mg
P0A
P=P0+ρgy
y
Area=A
Physics 207: Lecture 21, Pg 4
P1=P0+ρgy1
Pressure=P0
y1
P2=P0+ρgy2
y2
P2-P1=ρg(y2-y1)
Area=A
Physics 207: Lecture 21, Pg 5
What is the pressure 10m down?
P=P0+ρgy
=P0+(1000 kg/m3)(10 m/s2) (10 m)
=P0+105 N/m2
= approximately 2 atm
 Home exercise: what is the pressure 6 miles
down?
Physics 207: Lecture 21, Pg 6

Consider the open, connected container shown
below. How would the two heights compare?
A)y1<y2
B)y1=y2
C)y1>y2
y1
y2
Physics 207: Lecture 21, Pg 7
Pressure vs. Depth

In a connected liquid, the pressure is the same at
all points through a horizontal line.
p
Physics 207: Lecture 21, Pg 8
Pressure Measurements: Barometer
 Invented by Torricelli
 A long closed tube is filled with mercury
and inverted in a dish of mercury
 The closed end is nearly a vacuum
P0=ρgh
 Measures atmospheric pressure as
1 atm = 0.760 m (of Hg)
Physics 207: Lecture 21, Pg 9
Archimedes’ Principle
 Suppose we weigh an object in air (1) and
in water (2).
W1
W2?
How do these weights compare?
a) W1 < W2
b) W1 = W2
c) W1 > W2
Physics 207: Lecture 21, Pg 10
Buoyancy
y1
F1 y2
F2
F2=P2 Area
F1=P1 Area
F2-F1=(P2-P1) Area
=ρg(y2-y1) Area
=ρ g Vobject
=weight of the fluid
displaced by the
object
Physics 207: Lecture 21, Pg 11
Float or sink?

If we immerse the object completely in the liquid:
weight of the object < bouyant force
float
ρobject Vobject< ρfluid Vobject
float
ρobject < ρfluid
float

How does a steel ship float?
A)ρsteel < ρwater
B)overall density of the ship < ρwater
C) none of the above
Physics 207: Lecture 21, Pg 12
Float

If the object floats, then we can find the portion of the
object that will be immersed in the fluid
FB=mg
Vimmersed ρfluid g =Vobject ρobject g
FB
Vimmersed ρfluid =Vobject ρobject
Physics 207: Lecture 21, Pg 13
Pascal’s Principle
Any change in the pressure applied to an enclosed
fluid is transmitted to every portion of the fluid and to
the walls of the containing vessel.
Pressure=P0
y
P=P0+ρgy
Physics 207: Lecture 21, Pg 14
Pascal’s Principle in action:
Hydraulics, a force amplifier
F1
 Consider the system shown:
F2
 A downward force F1 is applied
to the piston of area A1.
 This force is transmitted through
the liquid to create an upward
force F2.
 Pascal’s Principle says that
increased pressure from F1
(F1/A1) is transmitted
throughout the liquid.
d2
d1
A1
A2
P1 = P2
F1 / A1 = F2 / A2
A2 / A1 = F2 / F1
Physics 207: Lecture 21, Pg 15
Fluid dynamics
 To describe fluid motion, we need something that describes
flow:
 Velocity v
 Ideal fluid model:
 Incompressible fluid.
 No viscosity (no friction).
 Steady flow
Physics 207: Lecture 21, Pg 16
Types of Fluid Flow
Physics 207: Lecture 21, Pg 17
Streamlines
 Keep track of a small portion of the fluid:
Physics 207: Lecture 21, Pg 18
Continuity equation
A
2
A
1
v
1
v
2
A1v1 : units of m2 m/s = volume/s
A2v2 : units of m2 m/s = volume/s
A1v1=A2v2
Physics 207: Lecture 21, Pg 19