1. Chapter 9
Solids and Fluids (c)

2. EXAMPLE
A small swimming pool has an area of 10 square meters. A wooden 4000-kg statue of density 500 kg/m3 is then floated on top of the pool. How far does the water rise?
Note: Density of water = 1000 kg/m3

3. Solution Given: rwood/rH20 = 0.5, A = 10 m2, M = 4000 kg Find: h h
Level is the same as if 4000 kg of water were added = 4 m3
Consider problem: A volume V = 4 m3 of water is added to a swimming pool. What is h?
= 40 cm

4. Quiz 1. What is your section number?
2. Three objects rest on bathroom scales at a lake bottom.
Object 1 is a lead brick of volume 0.2 m3
Object 2 is a gold brick of volume 0.2 m3
Object 3 is a lead brick of volume 0.1 m3
DATA: specific gravity of lead = 11.3
specific gravity of gold = 19.3
specific gravity of mercury = 13.6
Which statement is true?
a) #1 and #2 have the same buoyant force
b) #1 and #2 register the same weights on the scales
c) #1 and #3 have the same buoyant force
d) #1 and #3 register the same weights on the scales
e) If the lake were filled with mercury, the scales would not change.

5. Equation of Continuity
What goes in must come out!
mass density
Mass that passes a point in pipe during time Dt

6. Example Solution = 20 cm/s
Water flows through a 4.0 cm diameter pipe at 5 cm/s. The pipe then narrows downstream and has a diameter of of 2.0 cm. What is the velocity of the water through the smaller pipe?
Solution
= 20 cm/s

7. Laminar Flow and Turbulence
Laminar or Streamline Flow:
Fluid elements move along smooth paths that don’t cross
Friction in laminar flow is called viscosity
Turbulent flow
Irregular paths
Sets in for high gradients (large velocities or small pipes)

8. Ideal Fluids Laminar Flow Non-viscous Incompressible No turbulence
No friction between fluid layers
Incompressible
Density is same everywhere

9. Bernoulli’s Equation
Physical content: the sum of the pressure, kinetic energy per unit volume, and the potential energy per unit volume has the same value at all points along a streamline.
How can we derive this?

10. Bernoulli’s Equation: derivation
Physical basis: Work-energy relation
All together now:
With
We get:

11. Example: Venturi Meter
A very large pipe carries water with a very slow velocity and empties into a small pipe with a high velocity. If P2 is 7000 Pa lower than P1, what is the velocity of the water in the small pipe?

12. Solution
Given: DP = 7000 Pa, r = 1000 kg/m3
Find: v
v = 3.74 m/s

13. Applications of Bernoulli’s Equation
Venturi meter
Curve balls
Airplanes
Beach Ball Demo

14. Example a
Water drains out of the bottom of a cooler at 3 m/s, what is the depth of the water above the valve? b
Solution
Compare water at top(a) of cooler with water leaving valve(b).
= 45.9 cm

15. Three Vocabulary Words
Viscosity
Diffusion
Osmosis

16. Viscosity Viscosity refers to friction between the layers
Pressure drop required to force water through pipes (Poiselle’s Law)
At high enough velocity, turbulence sets in

17. Diffusion
Molecules move from region of high concentration to region of low concentration
Fick’s Law:
D = diffusion coefficient

18. Osmosis
Osmosis is the movement of water through a boundary while denying passage to specific molecules, e.g. salts