This document defines key concepts in fluid mechanics including: - Density, specific gravity, pressure, buoyancy, fluid flow, Bernoulli's principle. - Formulas are provided for calculating density, pressure, buoyant force, apparent weight. - Examples show calculations for problems involving the density, pressure, and buoyant force exerted by liquids on immersed objects.

1. DENSITY
• Density = mass / volume
• ρ = m / v
• ρ water = 1g/cm3
What is the density of a liquid if 75 cubic centimeters of its mass
of 93 grams?

2. SPECIFIC GRAVITY
• Relative Density
• SG = density of object/ density of water
The density of iron is 7850 kg/m3. What is the specific
gravity of iron related to water with density 1000 kg/m3 ?

3. •A block of lead has dimensions of 4.5
cm by 5.2 cm by 6 cm. The block
weighs 1587 g. From this information,
calculate the density and specific
gravity of lead.

4. PRESSURE
• Force per unit area
• P = F/A
• N/m2 = Pascal
• 1kPa = 1 atm
Calculate the pressure produced by a force of 800 N acting on an area of 2.0
m2.
The pressure of a gas contained in a cylinder with a movable piston is 300 Pa.
The area of the piston is 0.5 m2. Calculate the force that is exerted on the
piston.

5. •A brick delivery truck parks on a
roadside scale that measures 4 m by 6
m. If the brick truck weighs 60,000 N,
what pressure does the scale put on
the spring below?

6. LIQUID PRESSURE
• Calculate the water pressure on a diver as he
descends into a freshwater lake at (a) 5m
below the surface, (b) 35m below the surface.
• Explain why a dam is thicker at its base than at
its top.
PRESSURE = density of liquid x acceleration due to gravity x height

7. PASCAL’S PRINCIPLE
• An external pressure exerted on a static enclosed fluid is
transmitted uniformly throughout the volume of the fluid.
P1 = P2
𝐹1
𝐴1
=
𝐹2
𝐴2

8. The area of the small piston in a simple hydraulic lift is 50cm2
and is pushed down with a force of 50 N. How much force is
exerted upward by the large piston with an area of 2m2?
GIVEN: F1 = 50 N A1 = 50cm2 A2 = 2m2
Solution:
First, let’s make our units consistent:
50𝑐𝑚2
𝑥
1𝑚
100𝑐𝑚
2
= 5 𝑥 10−3
𝑚2
𝐹2 = 𝐹1
𝐴2
𝐴1
= 50
2
5 𝑥 10−3
= 20 000 𝑁

9. • A dentist’s chair makes use of Pascal’s principle to
move patients up and down. Together, the chair and
a patient exert a downward force of 2,269 N. The
chair is attached to a large piston with an area of
1,221 cm2. To move the chair, a pump applies force
to a small piston with an area of 88.12 cm2. What
force must be exerted on the small piston to lift the
chair?

10. ARCHIMEDES’ PRINCIPLE
An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.
Buoyancy – the apparent loss of weight of an object due to the buoyant force when it is
immersed in a fluid
Buoyant force – the net upward force that a fluid exerts on an immersed object, floating or
submerged
Buoyant Force = Weight of displaced object
= density of liquid x volume of displaced liquid x acceleration due to gravity
= ρ V g
Apparent weight = weight in liquid – weight in air
= ρVg - mg

11. If a container of sand has a volume of half a liter (500cm3),
and a mass of 0.83 kg, what is its apparent weight if it is
submerged in water?
Given: m = 0.83 kg ρ water = 1000 kg/m3
V = 500 cm3 = 0.0005 m3
Solution: The weight of the container is given by
W air = m g = (0.83 kg) (9.8 m/s2) = 8.1 N
According to Archimedes’ Principle
W fluid = ρVg = (1000 x 0.0005 x 9.8) = 4.9 N
Apparent weight = weight in liquid – weight in air
Apparent weight = 8.1 N – 4.9 N = 3.2 N

12. • A concrete slab weight 180N. When it is fully
submerged under the sea its apparent weight is
105N. Calculate the density of the sea water if the
volume of the sea water displaced by the concrete
slab is 4800 cm3

13. TWO TYPES OF FLUID FLOW
1. streamline or laminar flow – every particle
of liquid passing a particular point follows the
same path as the particles that passed the
point before.
2. Turbulent flow –characterized by agitated,
disorderly motion. Molecules of fluid swirl
and form whirlpool patterns called eddies.
FLUID DYNAMICS – moving fluids
FLUID FLOW: when the pressure is greater in one region of a fluid than in another, the
fluid flows from the high-pressure to the low-pressure region.

14. BERNOULLI’S PRINCIPLE
The pressure in a fluid decrease as the speed of the fluid
increases.
Bernoulli’s principle is a consequence of the conservation of energy. For a steady
flow of fluid there are 3 kinds of energy: the kinetic energy due to motion, potential
energy due to pressure, and the gravitational PE due to elevation. In a steady fluid
flow where no energy is added or taken away, the sum of these forms of energy
remains constant. If the elevation of the flowing fluid does not change, then an
increase in speed means a decrease in the pressure, and vice versa.