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Uncertainty Analysis

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Uncertainty Analysis
Dr. Jenahvive Morgan
Department of Civil and Environmental Engineering
Rowan University
Fall 2015
Fluid Mechanics - Buoyancy
 Buoyancy is the force that opposes the weight of
an immersed object. This force is exerted by a
fluid, either a liquid or a gas.
The Buoyant Force:
 On a body immersed in a fluid
 Is exerted upwards on the body
 Is equal to the weight of the fluid that the body
displaces.
The Buoyant Force:
 What are some applications of buoyancy?
The Buoyant Force:
 Goal: To understand buoyant force
 Initial Conditions: Atmospheric pressure exists at the
top of the water
 When the bottle is squeezed, what will happen to the
test tube?
 Will the test tube remain stationary?
 Will the test tube move?
 If the test tube moves, how will it move?
The Buoyant Force:
 Before squeezing the bottle, what is the Buoyancy
Force equal to?
FB
W
The Buoyant Force:
 Before squeezing the bottle, what is the buoyancy
force equal to?
FB  W
FB    g  Vdisplaced
The Buoyant Force: Think - Pair - Share
 Take a minute to think about what will happen to the
test tube.
 Then turn to your neighbor to discuss what will
happen to the test tube and why it happens.
 See if you can agree on an answer together.
The Buoyant Force: Think - Pair - Share
 What does happen to the test tube?
The Buoyant Force:
 What key variable has changed and how has that
variable changed?
FB
l1
l2
W
The Buoyant Force:
 What key variable has changed and how has that
variable changed?
FB
 Vdisplaced has become smaller.
Vdisplaced  ATube  (l1  l2 )
l1
l2
W
The Buoyant Force:
 When the bottle is squeezed, what happens to the
pressure in the bottle?
The Buoyant Force:
 When the test tube is sinking, what is the relationship
between FB &W ?
The Buoyant Force: HW Problem #1
 A floating block of wood has a metal part hanging by a
cord. The block of wood has dimensions of 40 x 40 x
10 mm and a specific gravity of S1 = 0.3. Find the
tension on the cord and the mass of the metal part, if
the metal part has a volume of 6200 mm3.
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Hint: Use Archimedes’ principle and the density of
water at 15oC is 999 kg/m3
FB1  Vsub1
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Weight of Object 1:
W1  S1V1
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Tension in the cord:
T  FB1  W1
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Buoyant Force of Object 2:
FB 2  Vsub2
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Weight of Object 2:
W2  T  FB 2
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Mass of the Metal Part:
W2 0.132 N
m2 

 13.46 g
m
g
9.81 2
s
2.5 mm
1
10 mm
2
Water, 15o C
The Buoyant Force:
 Take Aways:
 Buoyant force is equal to the weight of the fluid
that a body displaces in an immersed fluid.
 This force is exerted upwards on the body.
 The Buoyant force is exerted by a fluid, either a
liquid or a gas.
Center of Buoyancy
 Center of Gravity is the point in a body where the
gravitational force may be taken to act
 Center of Buoyancy is the center of the gravity of the volume
of water which a hull displaces
Drag Force
 The force exerted on a body, moving in a medium like
air or water, depends in a complex way upon the
velocity of the body relative to the medium, the
viscosity and density of the medium, the shape of
the body, and the roughness of its surface.
 The direction of the drag force is always opposite the
direction of the body's velocity.
Drag Force
 The most common method of mathematically
modeling the drag force is the equation:
1
2
FD  C D Av
2
FD = Drag Force, N
CD = Drag Coefficient, Dimensionless
A = Cross-sectional Area perpendicular to the flow,
m2
ρ = Density of the medium, kg/m3
v = Velocity of the body relative to the medium, m/s
Drag Force
 The Reynolds number has been found to be a useful
dimensionless number that can characterize the drag
coefficient's dependence upon the velocity. The Reynolds
number is basically the ratio of the inertial force of the
medium over its viscous force.
Re 
Lv

Re = Reynolds number, Dimensionless
L = Characteristic length of the body along the direction of
flow, m
μ = Dynamic Viscosity of the medium, N s/m2
ρ = Density of the medium, kg/m3
V = Velocity of the body relative to the medium, m/s
Drag Force HW Problem #2
 Look up the CD based on the shape and Reynolds
number
 If CD = 0.006 for a blimp at a Reynolds number greater
that 105, find the power to propel the blimp at 2 m/s.
The blimp is 1 m long and has a cross-sectional area of
45 m2. The density of the air is 1.112 kg/m3 and the
viscosity of the air is 1.75E-5 kg/ms.
Drag Force Example
Re 
Lv

1
2
FD  C D Av
2
Power  FV  1.2W  1.61E  3hp
Questions??
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