Chapter 9 Floating and Flow

I. Archimedes’ PrincipleA. Floating Objects

1) 300,000 ton metal ship floats while a 0.1 g pebble sinks2) Not weight, but density that matters

B. Archimedes’ Principle1) Density = mass/volume2) Mass = (volume)(density), so objects with the same volume can have

different masses, depending on how dense they are3) Buoyant Force = If you push down on a floating piece of wood, it pushes

back4) Archimedes’ Principle says buoyant force = weight of fluid displaced by

the submerged objecta) Fluid is more dense (water/wood) Buoyant Force > Weight of Woodb) Fluid is less dense (water, lead) Buoyant Force < Weight of Leadc) Wood Floats because it is less dense than waterd) Lead Sinks because it is more dense than water

C. Source of the Buoyant Force (FB)

1) Like the atmosphere, pressure is greatest at bottom of a fluid (water)

2) Larger pressure at the bottom produces a larger upward force than the downward force created by the smaller pressure at the top

3) Buoyant Force = difference between the top/bottom forces

D. Average Density

1) Why does a steel ship float? Steel is more dense than water/

2) In complex shapes, you must use the Average Density

3) The steel ship has many air pockets—density is much less than water

4) Average density of ship (steel + air) is less than water, so it floats

>

FB

E. Analyze Forces on a Sumberged Object

1) Average Density > Fluid Density

a) WO > FB

b) Object sinks

2) Average Density < Fluid Density

a) WO < FB

b) Object Floats

c) Just enough remains submerged so that Wo = FB

3) Average Density = Fluid Density

a) WO = FB

b) Object will stay submerged

c) Submarine or a fish

d) Object can sink or rise slowly by slightly changing its density

i. Submarine takes in water

ii. Fish change air bladder size

W

FB

II. Fluids in MotionA. Flowing Water

1) Continuity of Flow: same amount of water entering and exiting the stream or pipe at all times

2) Speed of the water increases as the stream/pipenarrows

a) Volume = L x A (A = W x H)

b) Rate of water flow = Volume/time = LA/t

c) Velocity of water flow = v = L/t

d) Rate of water flow = vA

3) If Area increases, v must decrease to keep rate of flow the same

4) If Area decreases, v must increase to keep the rate of flow the same

s

cmor

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t

Lrate

32

B. Viscosity and Flow

1) Flowing fluids can be thought of as having layers

2) Viscosity = frictional forces between those layers

a) Large viscosity = large friction (syrup or motor oil)

b) Small viscosity = small friction (alcohol or air)

3) Layers near edges move slower than the layers near the center

a) Low viscosity: speed reaches maximum quickly

b) High viscosity: speed reaches maximum only slowly

4) Viscosity of liquids >> Viscosity of gases

5) When you raise the Temperature, you lower the Viscosity

(motor oil, syrup)

C. Describing Flowing Fluids

1) Laminar Flow = layers of the fluid move parellel to each other

2) Turbulent Flow = layers move in disordered directions

a) Increases the resistance to flow (try to avoid for engineering )

b) Higher velocity leads to more turbulence

c) Lower viscosity leads to more turbulence

3) Transition between Laminar and Turbulent Flow is focus of research

III. Bernoulli’s PrincipleA. Apply Conservation of Energy to Flowing Fluids

1) If fluid is not compressed, work done on it has to result in increased KE

2) If KE increases, Velocity must increase = acceleration

3) Must be a net force to cause an acceleration

a) Difference in pressure between points in the fluid

b) Fluid is accelerated from high to low pressure

c) Higher velocity at low pressure area

4) Bernoulli’s Principle = Pressure + KE = constant for a fluid

B. Pressure variance in pipes or hoses

1) Pressure is lower at constricted areas (v, KE are higher)

constant2

1 2 vdPd = densityv = velocity

2fluid vd

2

1KE

If v1 is slow, KE is smallh1 = pressure = high

If v2 is fast, KE is largeh2 = pressure = low

2) Narrow nozzle on a hose

a) Pressure is actually lower at the nozzle than back in the hose

b) Velocity is higher at nozzle, momentum = mv is greater

c) p = Ft, you feel a stronger force because of velocity, not pressure

C. Airplane Wing

1) Larger velocity means lower pressure

2) Blow air above a strip of paper, the larger pressure below pushes the paper up into the low pressure area above it

3) Air going over the top of an airplane wing moves faster than the air going below the wing

4) Pressure above is less than the pressure below: Wing (and plane) lifted up

D. Suspended Ball

1) Air speed greatest at center (pressure is smallest)

2) Larger pressures outside keep ball centered

3) Upward force of blowing air keep it suspended