Physics 101: Lecture 18 Fluids II

1
Physics 101 Lecture 18 Fluids II

• Todays lecture will cover Textbook Chapter 9

• Hour Exam II
• Monday, Oct 29, 2007, 7 PM
• Conflict _at_ 515 sign up online
• Lectures 9-16
• Review session, Sunday, Oct 18, 8PM, 141 Loomis
• Conflict-conflict exams Prof. Ben Wandelt,
  bwandelt_at_uiuc.edu
• by tomorrow at noon

2
Review Static Fluids

• Pressure is force exerted by molecules bouncing
  off container P F/A
• Gravity affects pressure
• P P0 rgd
• Archimedes principle Buoyant force is weight
  of displaced fluid.
• F r g V
• Today include moving fluids!
• A1v1 A2 v2 continuity equation
• P1rgy1 ½ rv12 P2rgy2 ½rv22
  Bernoullis equation

Can demo
08
3
Archimedes Principle

• Buoyant Force (FB)
• weight of fluid displaced
• FB ?fluidVdisplaced g
• Fg mg ?object Vobject g
• object sinks if ?object gt ?fluid
• object floats if ?object lt ?fluid
• If object floats
• FB Fg
• Therefore ?fluid g Vdispl. ?object g Vobject
• Therefore Vdispl./ Vobject ?object / ?fluid

Al block demo
10
4
Preflight 1

• Suppose you float a large ice-cube in a glass of
  water, and that after you place the ice in the
  glass the level of the water is at the very brim.
  When the ice melts, the level of the water in the
  glass will
• 1. Go up, causing the water to spill out of the
  glass.
• 2. Go down.
• 3. Stay the same.

39 15 46
FB ?W g Vdisplaced FB W ?ice g Vice ? ?W
g Vmelted_ice
Must be same!
12
5
Preflight 2

• Which weighs more
• 1. A large bathtub filled to the brim with water.
  
• 2. A large bathtub filled to the brim with water
  with a battle-ship floating in it.
• 3. They will weigh the same.

16 25 59
Weight of ship Buoyant force Weight of
displaced water
15
6
Continuity
A four-lane highway merges down to a two-lane
highway. The officer in the police car observes 8
cars passing every second, at 30 mph. How many
cars does the officer on the motorcycle observe
passing every second? A) 4 B) 8
C) 16 How fast must the cars in the
two-lane section be going? A) 15 mph
B) 30 mph C) 60 mph
All cars stay on the road Must pass motorcycle
too
Must go faster, else pile up!
18
7
Continuity of Fluid Flow

• Watch plug of fluid moving through the narrow
  part of the tube (A1)
• Time for plug to pass point Dt x1 / v1
• Mass of fluid in plug m1 r Vol1
  r A1 x1 or m1 rA1v1Dt
• Watch plug of fluid moving through the wide
  part of the tube (A2)
• Time for plug to pass point Dt x2 / v2
• Mass of fluid in plug m2 r Vol2
  r A2 x2 or m2 rA2v2Dt
• Continuity Equation says m1 m2 fluid isnt
  appearing or disappearing
• A1 v1 A2 v2

22
8
Faucet Preflight

• A stream of water gets narrower as it falls from
  a faucet (try it see).
• Explain this phenomenon using the equation of
  continuity

Since the area inside the faucet is large, the
velocity of the water will be low. Due to the
equation of continuity, the area of the water has
to be lower due to the velocity increasing
outside of the faucet. (gosh darn i am sooooo
smart...but im still having trouble with the
quizzes....help me..)
Velocity and area are inversely proportional.
Velocity increases, so area decreases.
23
9
Fluid Flow Concepts
r
A1 P1
v1
A2 P2
v2

• Mass flow rate ?Av (kg/s)
• Volume flow rate Av (m3/s)
• Continuity ?A1 v1 ?A2 v2
• i.e., mass flow rate the same everywhere
• e.g., flow of river

24
10
Pressure, Flow and Work

• Continuity Equation says fluid speeds up going to
  smaller opening, slows down going to larger
  opening
• Acceleration due to change in pressure. P1 gt P2
• Smaller tube has faster water and LOWER pressure
• Change in pressure does work!
• W P1A1Dx1 - P2A2Dx2 (P1 P2)V

Recall WF d PA d P V
Venturi demo
28
11
Pressure ACT

• What will happen when I blow air between the
  two plates?
• A) Move Apart B) Come Together C) Nothing

Plate demo
Change in pressure does work on the plates.
31
12
Bernoullis Eqs. And Work

• Consider tube where both Area, height change.
• W DK DU
• (P1-P2) V ½ m (v22 v12) mg(y2-y1)
• (P1-P2) V ½ rV (v22 v12) rVg(y2-y1)
• P1rgy1 ½ rv12 P2rgy2 ½rv22

Note WF d PA d P V
34
13
Bernoulli ACT

• Through which hole will the water come out
  fastest?

P1rgy1 ½ rv12 P2rgy2 ½rv22
A
Note Outside all three holes the pressure is the
same P1 Atmosphere
B
P1 rgy1 P2 rgy2 y2 gt y1 ? P1 gt P2
C
Tank demo
Smaller y gives larger v. Hole C is fastest
37
14
Act

• A large bucket full of water has two drains. One
  is a hole in the side of the bucket at the
  bottom, and the other is a pipe coming out of the
  bucket near the top, which bent is downward such
  that the bottom of this pipe is even with the
  other hole, like in the picture below
• Though which drain is the water spraying out with
  the highest speed?
• 1. The hole
• 2. The pipe
• 3. Same

Speed is determined by pressure difference where
water meets the atmosphere. Relevant height is
where the hole is. Both are exiting at the same
height!
40
15
Example (like HW)

• A garden hose w/ inner diameter 2 cm, carries
  water at 2.0 m/s. To spray your friend, you place
  your thumb over the nozzle giving an effective
  opening diameter of 0.5 cm. What is the speed of
  the water exiting the hose? What is the pressure
  difference between inside the hose and outside?

Continuity Equation A1 v1 A2 v2 v2 v1 (
A1/A2) v1 ( pr12 / pr22)
2 m/s ? 16 32 m/s
Bernoulli Equation P1rgy1 ½ rv12 P2rgy2
½rv22 P1 P2 ½ r (v22 v12)
½ ? (1000 kg/m3) (1024 m2/s2 4 m2/s2
) 5.1 ? 105 Pa
16
Lift a House

• Calculate the net lift on a 15 m x 15 m house
  when a 30 m/s wind (1.29 kg/m3) blows over the
  top.

P1rgy1 ½ rv12 P2rgy2 ½rv22 P1 P2 ½
r (v22 v12) ½ r (v22 v12)
½ (1.29) (302) N / m2 581
N/ m2 F P A 581 N/ m2 (15 m)(15 m)
131,000 N 29,000 pounds! (note roof weighs
15,000 lbs)
48
17
Fluid Flow Summary

• Mass flow rate ?Av (kg/s)
• Volume flow rate Av (m3/s)
• Continuity ?A1 v1 ?A2 v2
• Bernoulli P1 1/2 ?v12 ?gh1 P2 1/2 ?v22
  ?gh2

50