Fluids ii
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Fluids II. F b. mg. Mg. Archimedes Example. A cube of plastic 4.0 cm on a side with density = 0.8 g/cm 3 is floating in the water. When a 9 gram coin is placed on the block, how much sinks below water surface?. h. 12. Question.

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Fluids II

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Fluids II


Fb

mg

Mg

Archimedes Example

A cube of plastic 4.0 cm on a side with density = 0.8 g/cm3 is floating in the water. When a 9 gram coin is placed on the block, how much sinks below water surface?

h

12


Question

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.

Must be same!

14


Archimedes’ Principle

  • If object is floating…

8


Archimedes’ Principle

  • Which picture looks like an ice cube floating?…

B

C

A

8


How much of the Iceberg can you see?


Tub of water + ship

Tub of water

Overflowed water

Question 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.

Weight of ship = Buoyant force =

Weight of displaced water

16


r

A1P1

v1

A2 P2

v2

Fluid Flow Concepts

  • 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

21


r

A1P1

v1

A2 P2

v2

Bernoulli’s Eq. And Work

  • W = DK + DU

  • W=F d = PA d = P V

    (P1-P2) V = ½ m (v22 – v12) + mg(y2-y1)

    (P1-P2) V = ½ rV (v22 – v12) + rVg(y2-y1)

    P1+rgy1 + ½ rv12 = P2+rgy2 + ½rv22

    Compare P1, P2

33


Example: 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.

48


Is Bernoulli’s Eq. involved in airfoil lift?


r

A1P1

v1

A2 P2

v2

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


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