1. Advanced Physics
Chapter 10
Fluids

2. Chapter 10 Fluids 10.1 Density and Specific Gravity
10.1 Density and Specific Gravity
10.2 Pressure in Fluids
10.3 Atmospheric and Gauge Pressure
10.4 Pascal's Principle
10.5 Measurement of Pressure
10.6 Buoyancy and Archimedes’ Principle
10.7 Fluids in Motion
10.8 Bernoulli’s Principle
10.9 Applications of Bernoulli’s Principle
10.10 Viscosity
10.11 Flow in Tubes
10.12 Surface Tension and Capillarity
10.13 Pumps; the Heart and Blood Pressure

3. 10.1 Density and Specific Gravity
10.1 Density and Specific Gravity
Four phases of matter (each with different properties)
Solid
Liquid
Gas
Plasma
Fluids are anything that can flow so they are ?

4. 10.1 Density and Specific Gravity
10.1 Density and Specific Gravity
Density- how compact an object is
Ratio of mass to volume
 = m/V
Many units for density
Specific Gravity- ratio of the density of a substance to the density of a standard substance (usually water)
No units (Why?)

5. 10.2 Pressure in Fluids P = F/A Pressure—a force applied per unit area
10.2 Pressure in Fluids
Pressure—a force applied per unit area
P = F/A
Units Pascal (N/m2)

6. 10.2 Pressure in Fluids Important properties of fluids at rest:
10.2 Pressure in Fluids
Important properties of fluids at rest:
Fluids exert a pressure in all directions
The force always acts perpendicular to the surface it is in contact with
The pressure at equal depths within the fluid is the same

7. 10.2 Pressure in Fluids P = F/A = gh P = gh
10.2 Pressure in Fluids
Pressure variation with depth
P = F/A = gh
Change in pressure with change in depth
P = gh

8. 10.3 Atmospheric and Gauge Pressure
10.3 Atmospheric and Gauge Pressure
Atmospheric Pressure (PA)—the pressure of the Earth's atmosphere at sea level
1atm = 101.3kPa = 14.7 lbs/in2 = 760 mmHg

9. 10.3 Atmospheric and Gauge Pressure
Gauge Pressure (PG)—the pressure measured on a pressure gauge
Measures the pressure over and above atmospheric pressure
P = PA + PG
P = Absolute pressure

10. 10.4 Pascal's Principle
Pascal's Principle states that pressure applied to a confined fluid increases the pressure throughout by the same amount
Example: hydraulic lift

11. 10.4 Pascal's Principle Pin = Pout Fout/Aout = Fin/Ain
Example: hydraulic lift
Pin = Pout
Fout/Aout = Fin/Ain
Fout/Fin = Aout/Ain
Fin

12. 10.5 Measurement of Pressure
Manometer—tubular device used for measuring pressure
To measure pressure with a manometer remember the Jenke quote “Nothing sucks in Science it just blows”

13. 10.5 Measurement of Pressure
Manometer—tubular device used for measuring pressure
Types:
Open-tube manometer
Closed-tube manometer (barometer)

14. 10.5 Measurement of Pressure
Open-tube manometer
both ends of tube are open; one is connected to the container of gas and the other is open to the atmosphere
GAS

15. 10.5 Measurement of Pressure
Open-tube manometer
P = Po + gh
Where:
P = pressure of gas
Po = atmospheric pressure
gh = pressure of fluid displaced
GAS

16. 10.5 Measurement of Pressure
Closed-tube manometer
one end of tube is open; one is connected to the container of gas is open and the other is sealed
GAS

17. 10.5 Measurement of Pressure
Closed-tube manometer
P = Po + gh
But since it is closed Po = 0 so…..
P = gh
GAS

18. 10.5 Measurement of Pressure
10.5 Measurement of Pressure
Barometer-closed-tube manometer inverted in a cup of mercury used to measure atmospheric pressure
P = gh
Where  is the density of mercury (13.6 x 103 kg/m2)

19. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Objects submerged in a fluid appear to weigh less than they do outside the fluid
Many objects will float in a fluid
These are two examples of buoyancy

20. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Buoyant force—the upward force exerted on an object in a fluid.
It occurs because the pressure in a fluid increases with depth

21. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Buoyant force (FB)
The net force due to the force of the fluid down (F1) and up (F2)
FB = F2 – F1
Since F = PA =FghA
FB = FgA(h2—h1)
FB = FgAh = FgV F1 h1 h2
h=h2-h1 F2

22. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Archimedes’ Principle
The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object
FB = FgV = mFg
To be in equilibrium the weight of object must be the same as the weight of fluid displaced so that it is equal and opposite FB FB
Wt = mg

23. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Archimedes’ Principle
So when an object is weighed in water its apparent weight (in fluid, w’) is equal to its actual weight (w) minus its buoyant force (FB)
w’ = w – FB
w/(w—w’) = o/ F FB
Wt = mg

24. 10.6 Buoyancy and Archimedes’ Principle
10.6 Buoyancy and Archimedes’ Principle
Archimedes’ Principle
Also relates to objects floating in fluid
Object floats in a fluid if its density is less than the density of the fluid
The amount submerged can be calculated by
Vdispl/Vo = o/ F
FB = FVdisplg
W= mg=oVog

25. 10.7 Fluids in Motion Fluid Dynamics (Hydrodynamics)
10.7 Fluids in Motion
Fluid Dynamics (Hydrodynamics)
The study of fluids in motion
Two types of fluid flow:
Streamline (laminar) flow--particles follow a smooth path
Turbulent flow—small eddies (whirlpool-like circles) form

26. 10.7 Fluids in Motion
Turbulent flow causes an effect called viscosity due to the internal friction of the fluid particles

27. 10.7 Fluids in Motion
Lets study the laminar flow of a liquid through an enclosed tube or pipe
Mass Flow rate is the mass of fluid (m) that passes a given point per unit time (t)
l1
l2 v1 v2 A2 A1

28. 10.7 Fluids in Motion Mass Flow rate
10.7 Fluids in Motion
Mass Flow rate
The volume of fluid passing through area A1 in time t is just A1 l1 where l1 is the distance the fluid moves in time t.
Since the velocity of fluid passing A1 is v = l1/ t, the mass flow rate m1/ t through area A1 is
m1/ t = 1A1v1
l1
l2 v1 v2 A2 A1

29. 10.7 Fluids in Motion Mass Flow rate m1/ t = 1A1v1
10.7 Fluids in Motion
Mass Flow rate
m1/ t = 1A1v1
Since what flow through A1 must also flow through A2 then
m1/ t = m2/ t So
1A1v1 = 2A2v2
l1
l2 v1 v2 A2 A1

30. 10.7 Fluids in Motion Mass Flow rate 1A1v1 = 2A2v2
10.7 Fluids in Motion
Mass Flow rate
1A1v1 = 2A2v2
Since for most fluids density doesn’t change (too much) with an increase in depth so it can be cancelled out.
Equation of continuity
A1v1 = A2v2
[Av] represents the volume rate of flow V/t of the fluid
l1
l2 v1 v2 A2 A1

31. 10.7 Fluids in Motion
Since the volume rate of flow V/t of the fluid is the same in all parts of the pipe the velocity through smaller diameter sections must be greater than through larger diameter sections
l1
l2 v1 v2 A2 A1

32. 10.8 Bernoulli’s Principle
10.8 Bernoulli’s Principle
Bernoulli’s Principle—where the velocity of a fluid is high, the pressure is low and where the velocity is low the pressure is high.
This makes sense; if the pressure was larger at A2 then it would back up fluid in A1 so its slow down from A1to A2 but it actually speeds up.
l1
l2 v1 P1 v2 P2 A2 A1

33. 10.8 Bernoulli’s Principle
10.8 Bernoulli’s Principle
Bernoulli’s Equation (derivation in Book)
P1 + 1/2v12 + gy1 = P2 + 1/2v22 + gy2 Or
P + 1/2v2 + gy = constant
This is based on the work needed to move the fluid from Part 1 to Part 2 of the tube.
l2 V2 P2 A2
l1 V1 P1 A1 y2 y1

34. 10.9 Applications of Bernoulli’s Principle
10.9 Applications of Bernoulli’s Principle
Special cases of Bernoulli’s Equation:
Liquid flowing out of an open container with a spigot at the bottom
Since both P’s are atmospheric pressure and v2 is almost zero
1/2v12 + gy1 = gy2
v1 = (2g(y2 – y1))1/2
V2 = 0
Y2 – y1 v1

35. 10.9 Applications of Bernoulli’s Principle
10.9 Applications of Bernoulli’s Principle
Special cases of Bernoulli’s Equation:
Liquid flowing but there is no appreciable change in height
P1 + 1/2v12 = P2 + 1/2v22
Example: your Physics toy

36. Read and Write Worksheet
Read and Write Worksheet
Read Sections –10.13
Answer the questions written on ½ sheet of paper