Fluids: statics and dynamics

In class Quiz #25-5
Suppose superman has infinite strength.
How high can he suck the liquid up?
(density of liquid is  )
1.
2.
3.
h = infinity h = 9.8 m h = P
0
/  g
Question from class:
Why can trees grow higher than 10 m?

http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_61/iss_1/76_1.shtml
Why can trees grow higher than 10 m?
Effective pore diameter inside leaves is 5-10 nm
(spacing between cellulose microfibrils)
Height of capillary water column with 10nm diameter is 3 km!
Why aren’t trees taller?
A: friction, bubbles
Capillary force
(electrostatic attraction of water to glass)
Redwood in CA

Last time: Buoyant Force (will it float?)

The magnitude of the buoyant force always equals the weight of the displaced fluid
B   V  fluid

The buoyant force is the same for a totally submerged object of any size, shape, or density
( remember V fluid means volume of fluid displaced by object )



The forces balance
 obj
 fluid

V fluid
V obj


If the object is less dense than the fluid, the object experiences a net upward force

If the object is more dense than the fluid the net force is downward

B   V  mg =
 object
V object g fluid
For completely submerged object:
V object
= V fluid
If
 object
<
 fluid
, mg < B
If
 object
>
 fluid
, mg > B

Example – P9.43
43. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density =
7.86

10 3 kg/m 3 ) is suspended from a spring scale and is completely submerged in the oil (Fig. P9.39). Find the equilibrium readings of both scales.

• A
1 v
1
= A
2 v
2
• The product of the cross-sectional area of a pipe and the fluid speed is a constant
– Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter
• Av is called the flow rate

• States that 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
P

1
 v
2
2
  gy
 constant

• Shows fluid flowing through a horizontal constricted pipe
• Speed changes as diameter changes
• Can be used to measure the speed of the fluid flow
• Swiftly moving fluids exert less pressure than do slowly moving fluids
P

1
 v 2
2
  gy
 constant

• The air speed above the wing is greater than the speed below
• The air pressure above the wing is less than the air pressure below
• There is a net upward force
– Called lift
• Other factors are also involved

h
1
=10.0 cm h
2
=5.00 cm
(along the way, find v
1 and v
2
!)