day of wrath

Physics 1B03summer-Lecture 12 1

Day of Wrath

Tuesday June 16

9:30-11:30 am

CNH-104

30 MC Questions, Cumulative


Fluid MechanicsFluid Mechanics

• Pressure• Buoyancy


BuoyancBuoyancyy

h

P1

P2

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 equalsthat of the force of gravity: B = Fg

so:

B = mg = ρoVog


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?

?


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


Example

A giant ice cube ( 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?


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?


Example:

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


Example

A 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 = ?


10 min rest


Fluid DynamicsFluid Dynamics

• Equation of Continuity• Bernoulli’s equation and examples


Fluid Dynamics

Approximations:

1) no viscosity (frictionless flow)

2) steady, “laminar” flow. If the flow is turbulent, mechanical energy is lost (converted to thermal energy).

3) “incompressible” fluid. Sufficiently accurate for gases if pressure differences are small.


StreamlineStreamliness

-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


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

1A1v1 = 2A2v2

Av = mass flow rate = constant

or for steady flow.

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

Volume flow rate = constant or A1v1 = A2v2


radius r1 = 10mm

radius r2 = 5mm

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 ?


Bernoulli’s Equation: work and energy in fluidsConditions: 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

2222

121

212

11 gyvPgyvP then,

or, streamline a alongconstant a221 gyvP

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


Example

a) 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


Example

What is the speed of the water leaving the hole in the tank? gauge pressure P0

h

v


ExampleWater 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


Exam Tips + Course Evaluations

day of wrath

Documents