AP Physics

II.A – Fluid Mechanics

Mass Density

Ex. What is the mass of a solid iron wrecking ball of radius 18 cm?The density of iron is 7800 kg/cubic meter.

Pressure

Consider the lowly tire

The force perpendicular to a given surface area is . . .

Increase pressure by

• Increasing force

• Decreasing area

For a static fluid, the force must be perpendicular, not parallel. Note that pressure is scalar.

Ex. A vertical column made of cement (density = 3000 kg/m3) has a base area of 0.50 m2. If its height is 2.0 m, how much pressure does this column exert on the ground?

Atmospheric pressure

Absolute Pressure

Note: hydrostatic pressure depends only on the density of the fluid and the depth of the

below the surface. The shape of the container is irrelevant.

The Hoover Dam

Ex. What is the gauge pressure and absolute pressure at a point 10.0 m below the surface of the ocean. The density of seawater is 1025 kg/m3.

Ex. Do both the gauge pressure and absolute pressure increase by a factor of two if the depth of an object below the surface of a liquid is doubled?

Ex. A flat piece of wood with an area of 0.50 m2 is lying at the bottom of a lake. If the depth of the lake is 30.0 m, what is the force on the wood due to the pressure?

II.A.2 Archimedes Principle (another incredible proof)

In words . . . Any fluid applies a buoyant force to an object that is

partially or completely submerged in the fluid. The magnitude of the force is equal to the weight of the

water displaced by the object.

But what about other forces?

So a battleship floats because . . .

Ex. An object with a mass of 150 kg and a volume of 0.75 m3 floats in ethyl alcohol (ρ = 800 kg/m3). What fraction of the object’s volume is above the surface of the fluid?

Ex. A brick with a mass of 3.0 kg and volume of 0.0015 m3, is dropped in swimming pool full of water. What is the normal force on the brick when it lays on the bottom of the pool?

Ex. A glass sphere with a density of 2500 kg/m3 and volume of 0.001 m3 is completely submerged in a large container of water. What is the apparent weight of the sphere while immersed?

Ex. A helium balloon has a volume of 0.03 m3. What is the net force on the balloon if it is surrounded by air? The density of helium is 0.2 kg/m3 and the density of air is 1.2 kg/m3.

II.A.3 – Flow Rate and The Equation of Continuity

Volume flow rate – if a fluid is incompressible, the volume of fluid that flows through a tube during a given time interval is

constant

Another proof

Since volume flow rate (Av) is constant, the speed is inversely

proportional to the cross-sectional area (i.e. the square of the radius).

Ex. A pipe of non-uniform diameter carries water. At one point in the pipe, the radius is 2.0 cm and the flow speed is 6.0 m/s. a) What is the flow rate? b) What is the flow speed at a point where the pipe constricts to a radius of 1.0 cm?

Ex. If the diameter of a pipe increases by a factor of 3, by what factor will the flow rate change?

II.A.4 Bernoulli’s Equation – complete with extended proof

Note that this horrible looking equation reduces to something much

simpler when a) the velocities are the same (or v = 0) or b) the fluid

conduit is horizontal

Bernoulli’s equation, Torricelli’s Theorem and efflux speed

Ex. Find the speed of water that leaves the spigot on a tank if thespigot is 0.500 m below the surface of water in the tank and thetank is open to the atmosphere.

Bernoulli’s Principle – pressure exerted by a fluid is inversely

proportional to its speed.

Some practical applications and astounding demos