• Fluids flow.

• Fluids are a collection of randomly arranged molecules held together by by weak cohesive forces. (Unlike crystals (solids) which arrange orderly on a lattice)

• Pressure, Pascal’s law

• Buoyant forces and Archimedes Principle

• Continuity equation

• Bernoulli’s equation

Chapter 14: Fluid mechanicsReading assignment: Chapter 15.1-15.3

Homework : (due Friday, Nov 4, 2005):

Problems: Q5, Q10, 1, 3, 7, 12, 20,

Buoyant forces and Archimedes's Principle

Archimedes’s principle:

The magnitude of the buoyant force equals the weight of the fluid displaced by the object.

gVgmF fffB

Imagine holding two bricks under water.Brick A is just beneath the surface of thewater, while brick B is at a greater depth.The force needed to hold brick B in place is

1. larger2. the same as3. Smaller

than the force required to hold brick A inplace.

A 200-ton ship enters the lock of a canal.The fit between the sides of the lock and theship is tight so that the weight of the waterleft in the lock after it closes is much lessthan 200 tons. Can the ship still float if thequantity of water left in the lock is much lessthan the ship’s weight?

1. Yes, as long as the water gets up to theship’s waterline.2. No, the ship touches bottom because itweighs more than the water in the lock.

An iron cube weighs 9.80 N in air.

How much does it weigh in water.

The density of iron is 7.86·103 kg/m3. The density of water is 0.998·103 kg/m3

Black board example 15.5

Archimedes’s principle

If density of object is less than density of fluid: Object rises (accelerates up)

If density of object is greater than density of fluid: Object sinks. (accelerates down).

Buoyant forces and Archimedes's Principle

Case 1:

Totally submerged objects.

gVFBF oofgtotal )(

Archimedes’ principle can also be applied to balloons floating in air (air can be considered a liquid)

Buoyant forces and Archimedes's Principle

Case 2:

Floating objects.

Buoyant force of displaced liquid is balanced by gravitational force.

Black board example 15.6

Homework 15.35

Archimedes’s principle

An ice slab has a thickness of 30.0 cm and a density of 917 kg/m3. When a 1100 kg car is resting on it the slab floats in water ( = 998 kg/m3) with its top at the same level as the water’s surface.

Find the area of the slab.

Two cups are filled to the same level withwater. One of the two cups has ice cubesfloating in it. Which weighs more?

1. The cup without ice cubes.2. The glass with ice cubes.3. The two weigh the same.

Two cups are filled to the same level withwater. One of the two cups has ice cubesfloating in it. When the ice cubes melt, inwhich cup is the level of the water higher?

1. The cup without ice cubes.2. The glass with ice cubes.3. It is the same in both.

Two cups are filled to the same level withwater. One of the two cups has plastic ballsfloating in it. If the density of the plastic ballsis less than that of ice, which of the two cupsweighs more?

1. The cup without plastic balls.2. The cup with plastic balls.3. The two weigh the same.

A boat carrying a large boulder is floatingon a lake.The boulder is thrown overboardand sinks. The water level in the lake (withrespect to the shore)

1. rises.2. drops.3. remains the same.

A lead weight is fastened on top of a largesolid piece of Styrofoam that floats in a containerof water. Because of the weight of thelead, the water line is flush with the top surfaceof the Styrofoam. If the piece of Styrofoamis turned upside down so that theweight is now suspended underneath it,

1. the arrangement sinks.2. the water line is below the top surface ofthe Styrofoam.3. the water line is still flush with the topsurface of the Styrofoam.

A lead weight is fastened to a large solidpiece of Styrofoam that floats in a containerof water. Because of the weight of thelead, the water line is flush with the top surfaceof the Styrofoam. If the piece of Styrofoamis turned upside down, so that theweight is now suspended underneath it, thewater level in the container

1. rises.2. drops.3. remains the same.

Consider an object floating in a container ofwater. If the container is placed in an elevatorthat accelerates upward,

1. more of the object is below water.2. less of the object is below water.3. there is no difference.

Consider an object that floats in water butsinks in oil.When the object floats in water,half of it is submerged. If we slowly pour oilon top of the water so it completely coversthe object, the object

1. moves up.2. stays in the same place.3. moves down.

In the following section we assume:

- the flow of fluids is laminar (not turbulent)

There are now vortices, eddies, turbulences. Water layers flow smoothly

over each other.

- the fluid has no viscosity (no friction). (Honey has high viscosity, water has low viscosity)

Equation of continuity

constant2211 vAvA

For fluids flowing in a “pipe”, the product of area and velocity is constant (big area small velocity).

Why does the water emerging from a faucet “neck down” as it falls?

A circular hoop sits in a stream of water, orientedperpendicular to the current. If thearea of the hoop is doubled, the flux (volumeof water per unit time) through it

1. decreases by a factor of 4.2. decreases by a factor of 2.3. remains the same.4. increases by a factor of 2.5. increases by a factor of 4.

Bernoulli’s equation

constant2

1 2 gyvP

22

2212

11 2

1

2

1gyvPgyvP

Conservation of energy

Black board example 15.7

Homework 15.51

Bernoulli’s law

Water flows through a horizontal pipe, and then out into the atmosphere at a speed of 15 m/s. The diameters of the left and right sections of the pipe are 5.0 cm and 3.0 cm, respectively.

(a) What volume of water flows into the atmosphere during a 10 min period?

(b) What is the flow speed of the water in the left section of the pipe?

(c) What is the gauge pressure in the left section of the pipe?

Two hoses, one of 20-mm diameter, the otherof 15-mm diameter are connected one behindthe other to a faucet. At the open endof the hose, the flow of water measures 10liters per minute. Through which pipe doesthe water flow faster?

1. the 20-mm hose2. the 15-mm hose3. The flow rate is the same in both cases.4. The answer depends on which of the twohoses comes first in the flow.