Physics Chapter 8 Fluid Mechanics

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PhysicsChapter 8Fluid Mechanics
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Density

• ? M
• V
• Therefore ?V M

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Density
Chapter 8
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Fig. T9.3, p. 262 Slide 13
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Archimedess Principle

• Any object completely or partially submerged
  in a fluid is buoyed up by a force whose
  magnitude is equal to the weight of the fluid
  displaced by the object.

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Buoyant Force

• The upward force is called the buoyant force
• The physical cause of the buoyant force is the
  pressure difference between the top and the
  bottom of the object

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Buoyant Force, cont.

• The magnitude of the buoyant force always equals
  the weight of the displaced fluid
• The buoyant force is dependent on the volume of
  the object and the density of the fluid it is
  submerged in.
• For a floating object, the buoyancy force must
  equal the weight of the object.
• BW
• Some objects may float high or low

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Example A balloon having a volume of 1.5 cubic
meters is filled with ethyl alcohol and is
tethered to the bottom of a swimming pool.
Calculate the tension in the cord tethering it to
the bottom of the swimming pool.

• Fy B T W 0
• Therefore, T B W
• T ?waterVg ?alcoholVg
• T (?water ?alcohol )Vg
• T (1000kg/m3 806kg/m3) (1.5m3)(9.8m/s2)
• T 2851.8 N

B
FBD
T
W
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11.6 Archimedes Principle
Example 9 A Swimming Raft The raft is made of
solid square pinewood. Determine whether the
raft floats in water and if so, how much of the
raft is beneath the surface.
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11.6 Archimedes Principle
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11.6 Archimedes Principle
The raft floats!
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11.6 Archimedes Principle
If the raft is floating
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Pressure

• P F N
• A m2
• Pascals Principal
• Pressure applied to a fluid in a closed
  container is transmitted equally to every point
  of the fluid and to the walls of the container.

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Hydraulic Lift
P1 P2 Therefore F1 F2
A1 A2
F2, A2
F1, A1
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Pressure at a Depth

• P F mg ?Vg ?Ahg ?hg
• A A A A
  

Find the pressure on the bottom of the submarine
due to the water above it. Find the pressure
on the bottom of the submarine due to the
water And air above it.
330 m
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Equation of Continuity

• A1v1 A2v2
• 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

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How Airplanes Wings Work