1 DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
2 OPTION B-3: LUIDS
3 Essential Idea: luids cannot be modelled as point particles. Their distinguishable response to compression from solids creates a set of characteristics that require an in-depth study.
4 Nature Of Science: Human understandings: Understanding and modelling fluid flow has been important in many technological developments such as designs of turbines, aerodynamics of cars and aircraft, and measurement of blood flow.
5 International-Mindedness: Water sources for dams and irrigation rely on the knowledge of fluid flow. These resources can cross national boundaries leading to sharing of water or disputes over ownership and use.
6 Theory Of Knowledge: The mythology behind the anecdote of Archimedes Eureka! moment of discovery demonstrates one of the many ways scientific knowledge has been transmitted throughout the ages. What role can mythology and anecdotes play in passing on scientific knowledge? What role might they play in passing on scientific knowledge within indigenous knowledge systems?
7 Understandings: Density and pressure Buoyancy and Archimedes principle Pascal s principle Hydrostatic equilibrium The ideal fluid Streamlines
8 Understandings: The continuity equation The Bernoulli equation and the Bernoulli effect Stokes law and viscosity Laminar and turbulent flow and the Reynolds number
9 Applications And Skills: Determining buoyancy forces using Archimedes principle Solving problems involving pressure, density and Pascal s principle Solving problems using the Bernoulli equation and the continuity equation
10 Applications And Skills: Explaining situations involving the Bernoulli effect Describing the frictional drag force exerted on small spherical objects in laminar fluid flow Solving problems involving Stokes law Determining the Reynolds number in simple situations
11 Guidance: Ideal fluids will be taken to mean fluids that are incompressible and non-viscous and have steady flows Applications of the Bernoulli equation will involve (but not be limited to) flow out of a container, determining the speed of a plane (pitot tubes), and venturi tubes
12 Guidance: Proof of the Bernoulli equation will not be required for examination purposes Laminar and turbulent flow will only be considered in simple situations Values of R 03 <will be taken to represent conditions for laminar flow
13 Data Booklet Reference: B V f f g P P 0 f gd Av cons tan t v gz p cons tan t D 6rv R vr
14 Utilization: Hydroelectric power stations Aerodynamic design of aircraft and vehicles luid mechanics is essential in understanding blood flow in arteries Biomechanics (see Sports, exercise and health science SL sub-topic 4.3)
15 Aims: Aim : fluid dynamics is an essential part of any university physics or engineering course Aim 7: the complexity of fluid dynamics makes it an ideal topic to be visualized through computer software
16 Reading Activity Questions?
17 Pressure Pressure, P, is defined as force per unit area where the force is understood to be acting perpendicular to the surface area, A pressure p A
18 Pressure in luids luid exerts a pressure in all directions luid pressure is exerted perpendicular to whatever surface it is in contact with luid pressure increases with depth
19 Pressure in luids Think of a disk 5 cm (0.05 m) in diameter (A = πr =.96 cm = m ) You place it in water 30 cm (0.30 m) below the surface The pressure on that disk is equal to the weight of a column of water that has a 5 cm diameter and is 30 cm high (h = height of water)
20 Pressure in luids Like a graduated cylinder A disk = m The volume of the cylinder is A x h (πr h) = 589 cm 3 = 5.89 x 0-4 m 3 V m m m V m x0 kg/ m 5.89x0 m 0.589kg
21 Pressure in luids Like a graduated cylinder A disk = m V = 5.89 x 0-4 m 3 m = kg ma mg 0.589kg 9.8m / s 5.78N
22 Pressure in luids Like a graduated cylinder A disk = m V = 5.89 x 0-4 m 3 m = kg = 5.78 N p A 5.78N m p.9x0 3 N / m That s way too much work! How about a formula?
23 Pressure in luids Like a graduated cylinder p A P =.9 x 0 3 N/m p mg A p Vg A That s way too much work! p Ahg A How about a formula? p gh
24 Pressure in luids Like a graduated cylinder P =.9 x 0 3 N/m p gh p.0x0 3 kg/ m 3 9.8m / s 0.3 m p.9x0 3 N / m That s way too much work! How about a formula? P gh
25 Pressure in luids Pressure at equal depths within a uniform liquid is the same p p 0 gh IMPORTANT: The pressure the water exerts on an object at a certain depth is the same on all parts of a body. In other words, if you hold a cube 30cm under water, each side of that cube will feel the same pressure exerted on it not just the top, but the bottom and all four sides!!!
26 Pressure in luids It follows from this that a change in depth is directly proportional to a change in pressure P gh P gh Note: An important assumption here is that the fluid is incompressible, because if it were compressible, the density would change with depth!
27 Pressure in luids P gh
28 Pascal s Principle The pressure applied to a confined fluid increases the pressure throughout the fluid by the same amount. Examples A cube at the bottom of a bucket of water. It has the pressure of the water acting on it, but also the atmospheric pressure pushing on the water. The brake system in a car. You apply pressure via the brake pedal and that pressure gets transmitted via a fluid to the brake pads on the wheel
29 Pascal s Principle P in P out The pressure applied to a confined fluid increases the pressure throughout the fluid by the same amount. A in in in out A out out A A in out out in A A out in
30 Pascal s Principle in out Examples A in A out
31 Pascal s Principle If I want the force applied to my brakes to be 0 times the force I apply to the pedal, by what factor would the diameter of the piston at the brakes exceed that of the piston at the brake pedal? out in A A out in
32 Pascal s Principle If I want the force applied to my brakes to be 0 times the force I apply to the pedal, by what factor would the diameter of the piston at the brakes exceed that of the piston at the brake pedal? out in 0x in in 0 x A A x 3.6 out in xr r
33 Video: Archimedes Principle
34 Buoyancy Stuff floats Stuff in water seems lighter than stuff on land This is because the fluid is exerting a pressure on the object that opposes the gravity force (weight) luid pressure increases with depth When the fluid pressure equals the weight, the object will stop sinking
35 Buoyant orce The force of fluid pressure that opposes weight P gh A gh gh A gh A
36 Buoyant orce The force of fluid pressure that opposes weight gh A gh A net net ga h h
37 Buoyant orce The force of fluid pressure that opposes weight net ga h h net gah cylinder net gv cylinder
38 Buoyant orce The force of fluid pressure that opposes weight net gv cylinder B gv cylinder
39 Archimedes Principle The force of fluid pressure that opposes weight net gv cylinder B gv cylinder The volume of the cylinder displaces the same volume of water that was there before the cylinder was immersed
40 Archimedes Principle The force of fluid pressure that opposes weight net gv cylinder B gv The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object
41 luids In Motion luid Dynamics study of fluids in motion Hydrodynamics study of water in motion Streamline or laminar flow flow is smooth, neighboring layers of fluid slide by each other smoothly, each particle of the fluid follows a smooth path and the paths do not cross over one another
42 luids In Motion Turbulent flow characterized by erratic, small whirlpool-like circles called eddy currents or eddies Eddies absorb a great deal energy through internal friction Viscosity measure of the internal friction in a flow
43 Speed Changes In Changing Diameter Of Tubes Assumes laminar flow low rate the mass (Δm) of fluid that passes through a given point per unit time (Δt) m t
44 Speed Changes In Changing Diameter Of Tubes m Mass is equal to density times volume t m V V m V t
45 Speed Changes In Changing Diameter Of Tubes The volume (V) of fluid passing that point in time (Δt) is the cross-sectional area of the pipe (A) times the distance (Δl) travelled over the time (Δt) t V V Al Al t
46 Speed Changes In Changing Diameter Of Tubes The velocity is equal to the distance divided by the time so, mass flow rate becomes ρav v Al t Av l t
47 Speed Changes In Changing Diameter Of Tubes Since no fluid escapes, the mass flow rate at both ends of this tube are the same Av A v
48 Speed Changes In Changing Diameter Of Tubes If we assume the fluid is incompressible, density is the same and, A v A v A v A v Equation of Continuity and Volume Rate of low
49 Speed Changes In Changing Diameter Of Tubes When cross-sectional area is large, velocity is small. When the crosssectional area is small, velocity is high A v A v A v A v Equation of Continuity and Volume Rate of low
50 Speed Changes In Changing Diameter Of Tubes That s why you put your thumb over the end of the hose to squirt people at car washes A v A v A v A v Equation of Continuity and Volume Rate of low
51 Bernoulli s Equation
52 Bernoulli s Equation Daniel Bernoulli (700-78) is the only reason airplanes can fly Ever wonder why: The shower curtain keeps creeping toward you? Smoke goes up a chimney and not in your house? When you see a guy driving with a piece of plastic covering a broken car window, that the plastic is always bulging out?
53 Bernoulli s Equation Ever wonder why: Why a punctured aorta will squirt blood up to 75 feet, but yet waste products can flow into the blood stream at the capillaries against the blood s pressure? How in the world Roberto Carlos made the impossible goal? It s Bernoulli s fault
54 Bernoulli s Principle
55 Bernoulli s Equation Bernoulli s principle states, where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high BLOWING PAPER DEMO Not as straight forward as it sounds Consider this,
56 Bernoulli s Equation We just said that as the fluid flows from left to right, the velocity of the fluid increases as the area gets smaller You would think the pressure would increase in the smaller area, but it doesn t, it gets smaller But, the pressure in area does get larger How come?
57 Bernoulli s Equation When you wash a car, your thumb cramps up holding it over the end of the hose. This is because of the pressure built up behind your thumb.
58 Bernoulli s Equation If you stuck your pinky inside the hose, you would feel pressure at the tip of your finger, a decrease in the pressure along the sides of your finger, and an increase in the velocity of the water coming out of the hose. You would also get squirted in the face but that s your own fault for sticking your finger in a hose!
59 Bernoulli s Equation It makes sense from Newton s Second Law In order for the mass flow to accelerate from the larger pipe to the smaller pipe, there must be a decrease in pressure A v A v ma P A
60 Bernoulli s Equation Assumptions: low is steady and laminar luid is incompressible Viscosity is small enough to be ignored Consider flow in the diagram below:
61 Bernoulli s Equation We want to move the blue fluid on the left to the white area on the right On the left, the fluid must move a distance of Δl Since the right side of the tube is narrower, the fluid must move farther (Δl ) in order to move the same volume that is in Δl
62 Bernoulli s Equation Work must be done to move the fluid along the tube and we have pressure available to do it W P d d A PA l W W P A P A l l
63 Bernoulli s Equation There is also work done by gravity (since the pipe has an increase in elevation) which acts on the entire body of fluid that you are trying to move orce of gravity is mg, work is force times distance, so: W W W d mg mgy y y mgy
64 Bernoulli s Equation Total work done is then the sum of the three: W T W W W 3 W T P A l P A l mgy mgy
65 Bernoulli s Equation Anything we can do to make this longer? W T W W W 3 W T P A l P A l mgy mgy
66 Bernoulli s Equation Anything we can do to make this longer? W T KE mv mv P A l P A l mgy mgy How about the work energy principle?
67 Bernoulli s Equation Better, but it needs to be cleaned up a little. m mv A l mv A P A l l P A l mgy mgy Substitute for m, then since A Δl = A Δl, we can divide them out
68 Bernoulli s Equation Manageable, mv v mv v P A l P P P A gy l gy mgy mgy but let s make it look like something a little more familiar
69 Bernoulli s Equation Look familiar, P v gy P v gy like Conservation of Energy?
70 Applications: Atomizers and Ping Pong Balls
71 Applications: Airfoils
72 Pitot-Prandtl Tube Measures airspeed by comparing static and dynamic pressure P static v v P dynamic air P dynamic P static
73 Viscosity A friction force between adjacent layers of fluid as the layers move past one another In liquids, it is mainly due to the cohesive forces between molecules In gases, it is caused by collisions between molecules. Coefficient of viscosity, η (lowercase eta) (Pa-s)
74 Viscosity Determined by measuring the force required to move a plate over a stationary one with a given amount of liquid between them
75 Coefficients of Viscosity Temperatures are specified because it has a strong effect on viscosity Viscosity for most fluids decreases rapidly with increase in temperature
76 Drag orce or a small sphere, the drag force is 6rv D The net force on a sphere falling through a fluid is Net mg 6 rv gv
77 Terminal Speed Terminal speed occurs when the net force is equal to zero 0 mg 6 rv gv 6 rv mg gv v mg 6 gv r
80 Reynolds Number A dimensionless number usually associated with aerodynamics for calculating drag vr Reynolds number for a pipe is, R Turbulence in pipes occurs at speeds when Reynolds number exceeds 000 v R 000 r
81 Understandings: Density and pressure Buoyancy and Archimedes principle Pascal s principle Hydrostatic equilibrium The ideal fluid Streamlines
82 Understandings: The continuity equation The Bernoulli equation and the Bernoulli effect Stokes law and viscosity Laminar and turbulent flow and the Reynolds number
83 Data Booklet Reference: B V f f g P P 0 f gd Av cons tan t v gz p cons tan t D 6rv R vr
84 Applications And Skills: Determining buoyancy forces using Archimedes principle Solving problems involving pressure, density and Pascal s principle Solving problems using the Bernoulli equation and the continuity equation
85 Applications And Skills: Explaining situations involving the Bernoulli effect Describing the frictional drag force exerted on small spherical objects in laminar fluid flow Solving problems involving Stokes law Determining the Reynolds number in simple situations
86 Guidance: Ideal fluids will be taken to mean fluids that are incompressible and non-viscous and have steady flows Applications of the Bernoulli equation will involve (but not be limited to) flow out of a container, determining the speed of a plane (pitot tubes), and venturi tubes
87 Guidance: Proof of the Bernoulli equation will not be required for examination purposes Laminar and turbulent flow will only be considered in simple situations Values of R 03 <will be taken to represent conditions for laminar flow
88 Essential Idea: luids cannot be modelled as point particles. Their distinguishable response to compression from solids creates a set of characteristics that require an in-depth study.
Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite
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