Understanding Fluid Statistics Basics GRADE 12

This presentation covers the essential principles of fluid statistics, including pressure distribution in fluids, buoyancy, and key applications in engineering and science. Perfect for students and professionals seeking a clear and concise overview of the topic.

1. FLUID STATICS

2. ENERGIZER

3. FLUIDS

4. A fluid is a substance that cannot withstand
shear stress and therefore flows under the
influence of gravity or an applied force.
Fluids include both liquids and gases.

5. Liquids: Fluids that have a definite volume but no definite shape. They take
the shape of their container.
Gases: Fluids that have neither a definite volume nor a definite shape. They
expand to fill their container.
Viscosity: A measure of a fluid’s resistance to flow. Higher viscosity means
thicker (more resistant to flow), while lower viscosity means thinner (less
resistant to flow).
Pressure: The force exerted per unit area within a fluid.
Flow Rate: The volume of fluid that passes through a given surface per unit
time.

6. Short History:
The concept of fluids has been studied for centuries, dating back to ancient civilizations
such as Greece and India. However, the modern understanding of fluids began to take
shape during the Scientific Revolution. include:
Archimedes: Known for his work on buoyancy and fluid displacement.
Robert Boyle: Conducted experiments on gases and formulated Boyle’s Law.
Daniel Bernoulli: Developed the Bernoulli equation, which describes the conservation of
energy in a flowing fluid.

7. DENSITY

8. DEFINITION
☆Density is a measure of how compact the mass in a substance is.
KEY TERMS
●Matter is any substance — solid, liquid, or gas.
●Mass is the measurement of how much matter is in an object.
●Volume is the measurement of how much space an object takes up.
●Density is the measure of how much matter is contained in a specific
volume.

Formula: p = m/V
p = density
m = mass
V = volume

9. Example # 1
A piece of gold has a mass of 115.92
grams and a volume of 6 cm3. What is
its density?

10. Example #2
The density of copper is 8.96 g/
cm3. A piece of copper has a
volume of 40cm3. What is its
mass?

11. PRESSURE

12. Pressure can be defined as the force exerted
by a fluid per unit area on a surface within the
fluid or on the boundaries containing the
fluid. It is a scalar quantity and acts equally in
all directions in a fluid at rest.
DEFINITION

13. •Short history
-Early (287–212 BCE) Archimedes established the fundamentals of buoyancy and
hydrostatics, which marked the beginning of the science of fluid mechanics.
Pascal's Law, which states that pressure in a confined fluid is transferred equally in
all directions, was developed by Blaise Pascal (1623-1662) in the 17th century,
furthering our understanding of pressure.
FORMULA
P: pressure
F: F is a force applied to an area
A: A that is perpendicular to the force

14. Example #1
A 15kg rectangular block with a
length of 70cm and a width of
40cm rests on a table. What
pressure does the book exert on
the table?

15. Example #2
A closed cylindrical container is
filled with a fluid that has a
specific gravity of 1.7. What is the
pressure exerted by this fluid at a
depth of 15m?

16. PRESSURE
CHANGE

17. Pressure is the weight of the
fluid mg divided by the area A
supporting it. (the area of the
bottom of the container):
P=mgA

18. Pressure
is the weight of the fluid mg divided by the area A supporting it (the area
of the bottom of the container)
The formula for pressure is:
P = mg/A
Short History
The study of pressure variation in fluids can be traced back to ancient
Greek philosophers like Archimedes, who explored buoyancy and
hydrostatics. In the 17th century, Blaise Pascal formulated the principle of
fluid pressure transmission (Pascal's Law). Daniel Bernoulli's work in the
18th century expanded our understanding of fluid dynamics and
hydrostatics, laying the foundation for modern fluid mechanics.

19. PASCAL’S
PRINCIPLE

20. PASCAL PRINCIPLE -ISAAC
DEFINITION
Pascal's Principle states that a change in pressure at any point in a confined fluid (liquid or
gas) is transmitted undiminished throughout the fluid and to the walls of the container.
HISTORY
1. Blaise Pascal (1623-1662)*: French mathematician and physicist.
2. 1653: Pascal conducted experiments with fluid pressure.
3."Traité de l'équilibre des liqueurs" (Treatise on the Equilibrium of Liquids)*: Pascal
published his findings in 1663.

21. FORMULA
P1/A1 = P2/A2
Where:
1. P1 and P2: Pressures at points 1 and 2.
2. A1 and A2: Areas at points 1 and 2.
KEY TERMS
1. Pressure transmission: Changes in pressure are transmitted equally in all directions.
2. Confined fluid: Liquids or gases enclosed within a container.
3. Equal pressure: Pressure remains constant throughout the fluid.
4. Force multiplication: Hydraulic systems can amplify forces.
DERIVATIONS
Pascal's Principle can be derived from:
1. Hydrostatic equilibrium: Fluids at rest.
2. Newton's laws: Conservation of momentum.
3. Continuity equation: Fluid flow.

22. Example #1
A hydraulic press has two cylinders, one with a radius of
2 cm and the other with a radius of 10 cm. A force of 100
N is applied to the smaller cylinder.

23. PART TWO

24. FLUID
DENSITY
PRESSURE
VARIATIONS OF PRESSURE
PASCAL’S PRINCIPLE

25. FLUIDS
Density
Viscosity
Surface tension
Pressure
Compressibility
Buoyancy
LIQUIDS
GAS
PLASMA

26. DENSITY
MASS per VOLUME
d=M/V
UNITS:
Kg/m
g/cm
3
3

27. PRESSURE
The force exerted
on an area
p=F/A
p=mg/A
p=dvg/A
v=Ah
p=dgh
Pressure(Pascals)=Force(New
tons)/Area(meters^2)
Pa=N/M^2
1000Pa=1Kpa
1000Kpa=1Mpa
1atm=101325Pa=101.3Kpa
1mmgh=1torr=133.32pa
1psi=6894.76pa

28. VARIATIONS OF PRESSURE WITH DEPTH
The change in
pressure due to
being submerged
in a fluid.
The change in
weight of the fluid.
pressure=Force/Area
Force=mass*gravity
density=mass/volume
volume=Area*height
pressure=density*
gravity*height
p=r*g*h / p=d*g*h

29. PASCAL’S PRINCIPLE
Pressure applied to
an enclosed fluid
will be applied
fully, equally, and
evenly to the
whole fluid up to its
container.
p1=p2
F1/A1=F2/A2
Win=Wout

30. GAUGE PRINCIPLE,
ABSOLUTE PRESSURE,
AND PRESSURE
MEASUREMENT

31. Gauge principle: Gauge pressure is the pressure relative to atmospheric
pressure. Gauge pressure is positive for pressures above atmospheric pressure,
and negative for pressures below it.
-Absolute pressure: Absolute pressure is the sum of gauge pressure and
atmospheric pressure
-pressure movement: force exerted by a fluid per unit area
KEY TERMS
Pabs = Pg + Patm
Pabs: absolute pressure
Pg: gauge pressure
Patm: atmospheric pressure

32. ARCHIMEDES’
PRINCIPLE

33. "The buoyancy force (or upward force) exerted on a body
immersed in a fluid is equal to the weight of the fluid displaced by
the body."
KEY TERMS
1. Archimedes' Principle: The buoyancy force equals the weight of
the fluid displaced.
2. Buoyancy: Upward force exerted by a fluid on an immersed
object.
3. Displacement: Volume of fluid shifted by the object.
4. Fluid: Liquid or gas surrounding the object.
5. Weight: Force due to gravity on the object.

34. Physical Quantities
1. Density (ρ): Mass per unit volume of the fluid.
2. Volume (V): Displaced fluid volume.
3. Gravity (g): Acceleration due to gravity (9.81 m/s²).
4. Buoyancy Force (Fb): Upward force on the object.
5. Weight (W): Force due to gravity on the object.
FORMULA
Fb = ρVg
Where:
1. Fb: Buoyancy force (N)
2. ρ: Fluid density (kg/m³)
3. V: Displaced fluid volume (m³)
4. g: Acceleration due to gravity (9.81 m/s²)

35. Calculations
1. Buoyancy force: Fb = ρVg
2. Displaced volume: V = (π * r² * h) for cylinders, or (4/3) * π * r³ for
spheres
3. Fluid density: ρ = mass / volume
Example
Calculate the buoyancy force on a cylindrical object:
1. Fluid: Water (ρ = 1000 kg/m³)
2. Object: Cylinder (r = 0.1 m, h = 0.5 m)
3. Displaced volume: V = π * (0.1)² * 0.5 = 0.0157 m³
4. Buoyancy force: Fb = 1000 * 0.0157 * 9.81 = 154.3 N
HISTORICAL CONTEXT
Archimedes discovered this principle in 250 BCE while bathing,
realizing the connection between fluid displacement and buoyancy.

38. COHESION AND
ADHESION

39. ●Attractive forces between
molecules of the same type are
called cohesive forces.
●Surface tension is the tendency of a liquid's
surface to contract due to the inward pull of
cohesive forces. Capillary action is the
movement of liquid within a narrow space driven
by the combined forces of adhesion (liquid-
surface attraction) and cohesion (liquid-liquid
attraction).

40. KEY CONCEPTS
* Surface Tension:
* Cohesive forces within a liquid create a "skin" on the surface. This
skin acts like an elastic membrane, minimizing the surface area.
* Examples:
* Insects walking on water
* Water droplets forming a spherical shape
* Capillary Action:
* The combined effect of cohesion and adhesion allows liquids to
rise or fall in narrow tubes (capillaries).
* Adhesion: The liquid is attracted to the walls of the tube.
* Cohesion: The liquid molecules stick together, pulling the column
of liquid upward.
* Examples:
* Water rising in a thin straw
* Water absorption by plants

41. QUIZ