AP Physics B. Fluid Dynamics. College Board Objectives. II. FLUID MECHANICS AND THERMAL PHYSICS A. Fluid Mechanics 1. Hydrostatic pressure Students should understand the concept of pressure as it applies to fluids, so they can: a) Apply the relationship between pressure, force, and area.
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II. FLUID MECHANICS AND THERMAL PHYSICS
A. Fluid Mechanics
1. Hydrostatic pressure
Students should understand the concept of pressure as it applies to fluids, so they can:
a) Apply the relationship between pressure, force, and area.
b) Apply the principle that a fluid exerts pressure in all directions.
c) Apply the principle that a fluid at rest exerts pressure perpendicular to any surface that it contacts.
d) Determine locations of equal pressure in a fluid.
e) Determine the values of absolute and gauge pressure for a particular situation.
f) Apply the relationship between pressure and depth in a liquid, DP = r g Dh
Students should understand the concept of buoyancy, so they can:
a) Determine the forces on an object immersed partly or completely in a liquid.
b) Apply Archimedes’ principle to determine buoyant forces and densities of solids and liquids.
3. Fluid flow continuity
Students should understand the equation of continuity so that they can apply it to
fluids in motion.
4. Bernoulli’s equation
Students should understand Bernoulli’s equation so that they can apply it to fluids in motion.
r for aluminum 2700 kg/m3 or 2.70 g/cm3
mass can be written as m = rV and
weight as mg = rVg
Specific Gravity: r substance / r water
5. (II) A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 88.78 g. What is the specific gravity of this other fluid?
Any fluid can exert a force perpendicular to its surface on the walls of its container. The force is described in terms of the pressure it exerts, or force per unit area:
Units: N/m2 or Pa (1 Pascal*)
dynes/cm2 or PSI (lb/in2)
1 atm = 1.013 x 105 Pa or 15 lbs/in2
*One atmosphere is the pressure exerted on us every day by the earth’s atmosphere.
Pressure varies with depth.
P = F = rAhg so P = rgh
A FLUID AT REST EXERTS PRESSURE PERPENDICULAR TO ANY SURFACE THAT IT CONTACTS. THERE IS NO PARALLEL COMPONENT THAT WOULD CAUSE A FLUID AT REST TO FLOW.
(b) What is the total force acting upward on the underside of the table?
9. (a) The total force of the atmosphere on the table will be the air pressure times the area of the table.
(b) Since the atmospheric pressure is the same on the underside of the table (the height difference is minimal), the upward force of air pressure is the same as the downward force of air on the top of the table,
p210.4 Atmospheric Pressure and Gauge Pressure
In this case, p2 is called the absolute pressure -- the total static pressure at a certain depth in a fluid, including the pressure at the surface of the fluid
The difference in pressure between the surface and the depth h is gauge pressure
Note that the pressure at any depth does not depend of the shape of the container, only the pressure at some reference level (like the surface) and the vertical distance below that level.
(a)The absolute pressure is given by Eq. 10-3c, and the total force is the absolute pressure times the area of the bottom of the pool.
Pout = Pin
And since P = F/a
Fout = Fin
Fout = Aout
10.(II) In a movie, Tarzan evades his captors by hiding underwater for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is calculate the deepest he could have been. (See page 261.)
10.The pressure difference on the lungs is the pressure change from the depth of water
This is an object submerged in a fluid. There is a net force on the object because the pressures at the top and bottom of it are different.
The buoyant force is found to be the upward force on the same volume of water:
The net force on the object is then the difference between the buoyant force and the gravitational force.
If the object’s density is less than that of water, there will be an upward net force on it, and it will rise until it is partially out of the water.
For a floating object, the fraction that is submerged is given by the ratio of the object’s density to that of the fluid.
This principle also works in the air; this is why hot-air and helium balloons rise.
22. The difference in the actual mass and the apparent mass is the mass of the water displaced by the rock. The mass of the water displaced is the volume of the rock times the density of water, and the volume of the rock is the mass of the rock divided by its density. Combining these relationships yields an expression for the density of the rock.
24.(a) When the hull is submerged, both the buoyant force and the tension force act upward on the hull, and so their sum is equal to the weight of the hull. The buoyant force is the weight of the water displaced.
floats on water. What minimum mass of lead, hung from the wood by a string, will cause it to sink?
34.For the combination to just barely sink, the total weight of the wood and lead must be equal to the total buoyant force on the wood and the lead.
If the flow of a fluid is smooth, it is called streamline or laminar flow (a).
Above a certain speed, the flow becomes turbulent (b). Turbulent flow has eddies; the viscosity of the fluid is much greater when eddies are present.
We will deal with laminar flow.
The mass flow rate is the mass that passes a given point per unit time. The flow rates at any two points must be equal, as long as no fluid is being added or taken away.
This gives us the equation of continuity:
If the density doesn’t change – typical for liquids – this simplifies to . Where the pipe is wider, the flow is slower.
A fluid can also change its height. By looking at the work done as it moves, we find:
This is Bernoulli’s equation. One thing it tells us is that as the speed goes up, the pressure goes down.
36. We apply the equation of continuity at constant density, Eq. 10-4b. Flow rate out of duct = Flow rate into room
At the website complete the following:1. Read and record important equations and facts.2. For each equation write the quantity for each symbol3. Write the unit for each quantity (symbol ok)