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Day of Wrath. Tuesday June 16 9:30-11:30 am CNH-104 30 MC Questions, Cumulative. Fluid Mechanics. Pressure Buoyancy. Buoyancy. The fluid exerts an upward force on the object equal to the weight of fluid displaced.

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day of wrath
Day of Wrath

Tuesday June 169:30-11:30 amCNH-104

30 MC Questions, Cumulative

Physics 1B03summer-Lecture 12

slide2

Fluid Mechanics

  • Pressure
  • Buoyancy

Physics 1B03summer-Lecture 12

slide3

Buoyancy

The fluid exerts an upward force on the object equal to the weight of fluid displaced.

This force is result of pressure differences in the fluid; the pressure is greater at the bottom than at the top.This is why objects can ‘float’: the magnitude of the buoyant force equals

that of the force of gravity:

P1

h

P2

B = Fgso:B = mg = ρoVog

Physics 1B03summer-Lecture 12

slide4

?

Archimedes’s Principle: the magnitude of the buoyant force always equals the weight of the fluid displaced by the object. Question: A boat filled with bricks floats in a swimming pool. If the bricks are dumped overboard does the water level in the pool rise, or fall?

Physics 1B03summer-Lecture 12

slide5
Totally Submerged Object

For an object submerged in a fluid with ρf the upward force is B=ρfVog (=weight of fluid displaced) and so the net force is:B – Fg = ρfVog - ρoVog = (ρf – ρo)Vog

Floating Object

For a floating object, it displaces a volume of fluid equal to its own volume, and so:

B = Fg

ρfVfg = ρoVog

Physics 1B03summer-Lecture 12

slide6

Example

A giant ice cube (r= 917 kg/m3) floats in a pail of cold water. If the cube is 100.0 mm on each side, how far is the top surface of the ice above the water?

When the ice melts, does the level of water in the pail rise or fall?

Physics 1B03summer-Lecture 12

slide7

Example

A beach ball of mass 0.05 kg and radius of 0.2 m is filled with air (density = 1.29 kg/m3) and placed under water.

a) What is the net force on the ball?

b) What is the acceleration of the ball?

Physics 1B03summer-Lecture 12

slide8

Example:How heavy a balloon can 100 litres of helium lift? (ρHe=0.18kg/m3)

Physics 1B03summer-Lecture 12

slide9

ExampleA 10-kg rock (density 2500 kg/m3) is suspended in a large bucket of water by a cord. What is the tension in the cord?

tension = ?

Physics 1B03summer-Lecture 12

10 min rest
10 min rest

Physics 1B03summer-Lecture 12

slide11

Fluid Dynamics

  • Equation of Continuity
  • Bernoulli’s equation and examples

Physics 1B03summer-Lecture 12

slide12

Fluid Dynamics

  • Approximations:
  • no viscosity (frictionless flow)
  • steady, “laminar” flow. If the flow is turbulent, mechanical energy is lost (converted to thermal energy).
  • “incompressible” fluid. Sufficiently accurate for gases if pressure differences are small.

Physics 1B03summer-Lecture 12

slide13

Streamlines

  • -the paths followed by particles in steady flow
  • velocity is parallel to the streamline
  • particles never cross streamlines; the streamlines mark out imaginary “tubes of flow”

area A1

speed v1

area A2

speed v2

Physics 1B03summer-Lecture 12

slide14

Equation of Continuity

“Volume flow rate” (volume per unit time)

= (cross-sectional area)  (linear velocity)

“Mass flow rate” (mass per unit time)

= (density)  (volume flow rate)

So, if mass in = mass out, then

rAv =mass flow rate=constant

r1A1v1 =r2A2v2

or

for steady flow.

“Incompressible” fluids (density remains uniform): cancel out density to get

A1v1 =A2v2

or

Volume flow rate =constant

Physics 1B03summer-Lecture 12

slide15

A fluid if flowing through a pipe of 10mm radius at a velocity of 10m/s. How fast will it be flowing if the pipe narrows to 5mm in radius ?

radius

r2 = 5mm

radius

r1 = 10mm

Physics 1B03summer-Lecture 12

slide16

Bernoulli’s Equation: work and energy in fluids

Conditions: steady flow, incompressible fluid.

Look at energy balance along a streamline:

Change in (kinetic energy/volume)

+ change in (potential energy/volume)

= (net work by pressure)/volume

then,

or,

Note: the above equation looks similar what we have seen before if we replace ρ by m.

Physics 1B03summer-Lecture 12

slide17

Examplea) What is the velocity of the water leaving the little hole

b) How far (horizontally) from the hole does the water hit the ground?

d

h

x

Physics 1B03summer-Lecture 12

slide18

Example

What is the speed of the water leaving the hole in the tank?

gauge pressure P0

h

v

Physics 1B03summer-Lecture 12

slide19
Example

Water moving at 10m/s through a 1m radius pipe at a pressure of 50kPa. It then falls 50m and goes into a 0.3m radius pipe. What is the water pressure at the bottom ?

h

Physics 1B03summer-Lecture 12

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Physics 1B03summer-Lecture 12

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