Transcript In Class Notes - Hydrostatics and Buoyancy

HYDROSTATICS
FLUIDS AT REST
OBJECTIVES
1.
Define and apply the concepts of density and fluid pressure to solve
physical problems.
2.
Define and apply concepts of absolute, gauge, and atmospheric
pressures.
3.
State Pascal’s law and apply for input and output pressures.
4.
State and apply Archimedes’ Principle to solve physical problems.
WHAT IS A FLUID?
DENSITY VS. MASS DENSITY
What is Density?
• density is a measure of a quantity of a substance in a given space
How is it different than Mass Density?
• mass density measures the mass of a substance in a given space ~ we will use
this!
COMMON DENSITY’S
SPECIFIC GRAVITY
The specific gravity rr of a material is the ratio of its density to the density of
water (1000 kg/m3). No Units!
Why would know specific gravity of a substance be a useful measurement?
r 
x
Steel (7800 kg/m3)
r = 7.80
1000 kg/m3
Brass (8700 kg/m3)
r = 8.70
Wood (500 kg/m3)
r = 0.500
QUESTION
Six objects (A-F) are in a liquid, as shown. None of them are
moving. Arrange them in order of density, from lowest to
highest.
ANSWER
Full answer to the question: B, D, A, F, E, C.
The more of an object's volume is above the water
surface, the less dense it is. Object B must
therefore be the least dense, followed by D, A, and
F. Object E is next, because it is neutrally buoyant
and equal in density to the liquid. Object C is
negatively buoyant because it is more dense than
the fluid.
QUESTION:
Why do things feel lighter in water than they do in air?
ANSWER: The reason is that a fluid exerts an upward force on objects that
are partially or completely submerged in it. This upward force is called a
buoyant force.
BUOYANT FORCE
1. Acts in the opposite Direction of the Force of gravity
2. Net force acting on an object is therefore ALWAYS smaller than zero
3. The weight of an object in water is it’s apparent weight
4. If the objects Specific Gravity is less than 1, the buoyant force is larger
than gravity and therefore an object floats!
ARCHIMEDES PRINCIPLE
Any object completely or partially submerged in a fluid experiences an
upward buoyant force equal in magnitude to the weight of the fluid
displaced by the object.
CONFUSING!
SINKING VS. FLOATING
QUESTION
A cube of steel that measures 5.0 cm on
each side is immersed in water. The density
of steel is 9.0 x 103 kg/m3. The density of
water is 1.0 x 103 kg/m3. What is the….
(a) buoyant force acting on the cube? and…
(b) its apparent weight?
ANSWER:
(a) Find the buoyant force.
The volume of the cube is:
(b) Find the apparent weight.
The weight of the cube is:
Now we can plug and chug:
To find the apparent weight we use this equation:
FA = FW - FB = 110 N -12 N
=
98 N
Extra Questions:
1. A 2.8 kg rectangular air mattress is 2.00 m long, 0.500 m
wide, and 0.100 m thick. What mass can it support in
water before sinking?
2. A ferry boat is 4.0 m wide and 6.0 m long. When a truck
pulls onto it, the boat sinks 4.00 cm in the water. What is
the weight of the truck?
3. An empty rubber balloon has a mass of 0.0120 kg. The
balloon is filled with helium at 0°C, 1 atm pressure, and a
density of 0.179 kg/m3. The filled balloon has a radius of
0.500 m.
a. What is the magnitude of the buoyant force acting on the
balloon? (Hint: See Table 1 for the density of air.)
b. What is the magnitude of the net force acting on the
balloon?
ANSWERS
1. 97kg
2. 9.4×103N
3. a. 6.63 N b. 5.59 N
PRESSURE
What is pressure?
Pressure is a measure of how much force is
applied over a given area.
PASCAL’S PRINCIPAL/PASCAL’S LAW
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.
HYDRAULIC LIFT
The key: Pressure is equal at both points of the lift
QUESTION
The small piston of a hydraulic lift has an area of 0.20 m2. A car weighing
1.20 x 104 N sits on a rack mounted on the large piston. The large piston
has an area of 0.90 m2. How large a force must be applied to the small
piston to support the car?
ANS: F1 = 2.7 x 103 N
DEPTH
Why are submarine hulls made of thick layers of titanium or steel?
Pressure in fluids increases with depth! We can derive this from our
pressure formula.
Gauge Pressure:
FLUID PRESSURE AS A FUNCTION OF DEPTH
Atmospheric Pressure: P0 = 1.0 x 105 Pa
CONNECTING BUOYANT FORCE TO PRESSURE
Explain why the force at the bottom
of the object is greater than at the
top of the object.
ANS: at greater depth the pressure
is great resulting in a great force on
the bottom than the top
QUESTION 1:
A diver is located 20 m below the
surface of a lake (ρ = 1000 kg/m3).
What is the gauge pressure due to
the water?
ΔP = 196 kPa
What is the absolute pressure?
ΔP = 296 kPa
h
ρ = 1000 kg/m3
QUESTION 2:
A 2-kg brass block is attached to a string and
submerged underwater. Find the buoyant force and
the tension in the rope. Include a Force diagram!
Density = 8700 kg/m3
FB + T = mg
FB = ρwgVw
T
FB = gV
FB = 2.25 N
T = 17.3 N
Force diagram
mg