This document discusses key concepts in fluid mechanics including: - Density is the ratio of mass to volume and is measured in kg/m3. - Pressure is force per unit area and is measured in units of N/m2 or Pa. - Pascal's principle states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. - Bernoulli's principle states that as the velocity of a fluid increases, its pressure decreases.

1. MECHANICS OF FLUIDS

2. FLUIDS
Anything that can flow
Liquid and Gases
Fluid DynamicsFluid Static
- Study of fluids in
motion
- study of fluids at
rest

3. Density
- ratio of mass of a substance
to its volume
V
m
=ρ
ρ = density
m = mass
V = volume
Unit:
kg/m3

4. Density
When the can is squeezed, the
density increases.
What will
happen to its
density?

5. Density

6. Pressure
- force per unit area
A
F
P =
P = pressure
F = force
A = area
Unit:
N/m2
or Pa

7. Pressure

8. Pressure

9. Pressure
It is the same any particular depth
in liquid contained in vessels of
different sizes or shape.
12 Pa
12 Pa
12 Pa

10. 1. Pascal’s Principle
The pressure applied at
any given point on a
confined fluid is
transmitted undiminished
throughout the fluid.
Application

11. 1. Pascal’s Principle
The pressure applied at any given point
on a confined fluid is transmitted undiminished
throughout the fluid.
Application
This is much
better!

12. 1. Pascal’s Principle
The pressure applied at any given point
on a confined fluid is transmitted undiminished
throughout the fluid.
2
2
1
1
21
A
F
A
F
PP
=
=

13. 1. Pascal’s Principle
F1 = 2500 N F2 = ? W = 10000 N
A1 = 2 m2
A2 = 8 m2
2
2
1
1
21
A
F
A
F
PP
=
=

14. 2. Bernoulli’s Principle
- As the velocity of the fluid
increases, its pressure decreases

15. Buoyancy
The fluid always go from high
pressure area to low pressure
area
What will happen if the train passes on
your side?
Lower velocity
Higher pressure
Higher velocity
Lower pressure

16. Buoyancy
- upward force when object is
submerge in fluid
Buoyant force

17. 3. Archimedes’ Principle
A body partly or entire submerged
in a fluid is buoyed up by a force
equal in magnitude to the weight of
the displaced fluid.
BF = Wair - Wwater
BF = Wfluid displaced

18. Problems
1. An 80 kg metal cylinder 2m long and with each
end of area 25 cm2
stands vertically on one end.
What pressure does the cylinder exert on the
floor?
2. A piston of cross-sectional area "a" is used in
a hydraulic press to exert a small force of
magnitude "f" on the enclosed liquid. A
connecting pipe leads to a larger piston of cross-
sectional area A. If the piston diameters are 3.80
cm and 53.0 cm, what force magnitude on the
small piston will balance a 20.0 kN force on the
large piston?

19. Problems
3. What is the maximum weight a solid, square,
pinewood raft measuring 4.0 m on a side and
0.30 m thick support and still float in water? How
much weight can we add in the raft so that it can
still float? ρwood = 420 kg/m3
4. A solid aluminum cylinder, ρ = 2700 kg/m3
weighs 0.067 kg in air and 0.045 kg in turpentine.
Determine the density of the turpentine.