Chapter 14 Fluids. Fluids at Rest (Fluid = liquid or gas)
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Transcript of Chapter 14 Fluids. Fluids at Rest (Fluid = liquid or gas)
Chapter 14
Fluids
Fluids at Rest
(Fluid = liquid or gas)
Density ()
• unit: kg/m3
• we will consider only = m/V = constant
• (incompressible fluid)
• we will also assume g = constant
dV
dm
Pressure (p)
• A fluid exerts a force dF normal to any area dA you consider in it.
• For a fluid at rest, the force is equal and opposite on each side.
Pressure (p)
• Why is there a force?
• Microscopically: the fluid particles are in motion and collide with dA
• Macroscopically: the fluid is at rest
Pressure (p)
• pressure p is a scalar (no intrinsic direction)
• reason: it acts normal to any surface dA
dA
dFp
Pressure (p)
• units used:pascal, millibar, atm
• 1 Pa = 1 N/m2
1 millibar = 100 Pa 1 atm = 1.013×105 Pa
dA
dFp
Terminology
• ‘gauge pressure’ = p – patm
• (can be > 0 or < 0)
• (e.g., read on a car tire pressure gauge)
• p = absolute pressure (> 0) = atmospheric pressure + gauge pressure = patm + gauge pressure
Pressure and depth
gdy
dp
• pressure: p coordinate: y
• pressure decreases with ‘elevation’ y:
Derive this result and integrate itDerive this result and integrate it
Pressure and depth
ghpp
yygpp
21
1212 )(
• coordinate: y distance: h > 0
• p increases with depthfor any shape of vessel
Demonstration: depth and shape of containerDemonstration: depth and shape of container
Exercise 14-10
• The dangers of a long snorkel tube:
• Find the gauge pressure at the depth shown. Will this cause the snorkeler’s lungs to collapse?
Demonstration: atmospheric pressureDemonstration: atmospheric pressure
Pascal’s Law
ghpp
yygpp
21
1212 )(
• If any change in pressure p is applied at one point, it is transmitted to all points in the fluid and to walls enclosing it.
Example: Hydraulic Lift At equilibrium, p = F1/A1 = F2/A2
DemonstrationDemonstration
Two Pressure Gauges
Notes on (a) and Exercise 14-9Notes on (a) and Exercise 14-9Notes on (b) firstNotes on (b) first
Homework Hints: Exercise 14-55
Buoyancy and Buoyant Force
A (fully or partially) submerged object feels an upward force equal to the weight of fluid it displaces
(a) fluid element with weight wfluid
(b) body of same shape feels buoyant force B = wfluid
DemonstrationDemonstration
Surface Tension• Molecules of liquid
attract each other (else no definite volume)
• center: net force = 0
• surface: net force is directed inward
Surface Tension• So the surface acts like a
membrane under tension (like a stretched drumhead)
• The surface resists any change in surface area
• Strength characterized by ‘surface tension’
DemonstrationDemonstration
Surface Tension • = F/d
= cohesive force per unit length
• surface tension force F = d
• We can measure by just balancing F
Do Example 14-23 Do Example 14-23 Notes on measuring Notes on measuring
cohesion: attraction of like molecules example: liquid-liquid forces (surface tension)
adhesion: attraction between unlike moleculesexample: liquid-glass forces
(a) adhesion > cohesion: water wets glass(b) adhesion < cohesion: mercury beads up
Capillarity
• For these two cases, the surface tension force F pushes the column of liquid either up or down:
• (a) up for water• (b) down for mercury
Notes on capillary tubesNotes on capillary tubes
Homework Announcements
• Homework Set 5: Correction to hints for 14-55 (handout at front and on webpage)
• Recent changes to classweb access (see HW 5 sheet at front and webpage)
• Homework Sets 1, 2, 3: returned at front(scores to be entered on classweb soon)
Midterm Announcements
• Friday:
• review required topics
• practice problems (from class, HW, new?)
• Monday: (midterm)
• you can bring a sheet of notes (both sides)
• you will be given a list of equations
Fluid Flow
(Fluid Dynamics)
Flow Fluid
• Flow line =path of fluidelement
• Flow tube =bundle of flow lines passingthrough area A (just a useful construct)
Simplifying Assumptions
• Steady flow:
• At any given point in the fluid, its properties (v, , p) don’t change in time
Simplifying Assumptions
• Steady flow:
• different flow lines never cross each other
• fluid entering a flow tube never leaves it
Simplifying Assumptions
• Incompressible fluid:
• = constant
• No friciton:• no ‘viscosity’
Continuity Equation
A1v1 = A2v2 • the same volume dV of
fluid enters and exits tube:
• dV = volume passing through A in dt = Av dt
Avdt
dV
NotesNotes
Continuity Equation
A1v1 = A2v2
• along the flow: • A = area of flow tube
v = speed of fluid
• if one increases, theother must decrease
Notes and Demonstration: water flowNotes and Demonstration: water flow
Continuity Equation
A1v1 = A2v2
• Where the flow lines are crowding together, the fluid speed is increasing
Bernoulli’s Equation
• only valid for: steady flow, incompressible fluid,no viscosity!
2222
2111
2
1
2
1
vgyp
vgyp
NotesNotes
Bernoulli’s Equation
• if v1= v2= 0:
• reduces to previous result for fluid at rest
2222
2111
2
1
2
1
vgyp
vgyp
Bernoulli’s Equation
• if y1= y2 then for p and v:
• if one increases, theother must decrease
2222
2111
2
1
2
1
vgyp
vgyp
DemonstrationDemonstration
Applications of Bernoulli’s Equation
Venturi Meter (Example 14-10) horizontal flow tube
NotesNotes
Note: if viscosity is present, then v decreases with distance from tube center
Venturi Meter:Homework Problem 14-90 (c)
NotesNotes
DemonstrationDemonstration
Wing Lift
Can’t predict flow lines but they indicate low pressure above wing, so net force up
Demonstration: propellorDemonstration: propellor
Efflux Speed: vertical flow tube
NotesNotes
Siphon: flow tube points up, then down
• First: you must fill the tube
• There is a limit:
H + h < 10 m
Curve Ball: viscosity makes it possible
Warm-up demonstrationsWarm-up demonstrations
Viscosity drags air with spinning ball: low pressure=net force so the ball curves
DemonstrationDemonstration
Homework Announcements
• Homework Set 5: Correction to hints for 14-55 (handout at front and on webpage)
• Recent changes to classweb access (see HW 5 sheet at front and webpage)
• Homework Sets 1, 2, 3: returned at front(scores to be entered on classweb soon)