13.19 - Summary
Fluids are substances, liquids and gases, that can flow and conform to the shape of
the container that holds them.
A material’s density is the amount of mass it contains, per unit volume. Density is
represented by the Greek letter ȡ and has units of kg/m^3. Unless otherwise stated,
substances are assumed to be of uniform density, which means they have the same
density at all points.
Pressure is the amount of force on a surface per unit area. The unit of pressure is
the pascal (Pa), which is equal to 1 N/m^2.
Fluids can exert forces, and therefore pressure, just as solid objects can. For an
object immersed in a liquid, the pressure is the product of the liquid’s density, the
acceleration of gravity g, and the object’s depth. Gauge pressure is the pressure
due solely to the liquid, while absolute pressure is the pressure of the liquid plus
atmospheric pressure.
Buoyancy is the upward force that results when an object is placed in a fluid, the
force that causes a ship to float. Archimedes’ principle states that the magnitude of
the buoyant force is equal to the weight of the fluid displaced by the object.
Pascal’s principle applies to confined fluids. It states that an enclosed fluid will
transmit pressure unchanged in all directions.
To simplify the study of fluid flow, we often assume an ideal fluid flow. This means
that the flow is streamline flow í it has a constant velocity at every fixed point í and
that it is irrotational. The fluid is also assumed to be incompressible and nonviscous.
One property of ideal fluid flow is stated by the fluid equation of continuity. The
amount of fluid flowing past every point in a closed system is the same. In other
words, the volume flow rate is constant regardless of the size of the area through
which the fluid flows.
Another property of ideal fluid flow is described by Bernoulli’s equation. The sum of
the pressure, kinetic energy density, and potential energy density is constant in a
closed system. For horizontal flow, the faster a fluid flows, the lower its pressure.
This is called the Bernoulli effect.
The atmosphere exerts pressure because it is a fluid. But since it is a gas, air
density and pressure decrease noticeably with altitude. Despite often being ignored
in day-to-day life, air pressure is actually (and demonstrably) quite large.
Surface tension is an effect seen with certain liquids such as water. Polar molecules
on the surface of the liquid are attracted toward the interior by unbalanced
intermolecular forces, causing the surface to contract, and consequently to minimize its own area and exhibit some elastic-like properties.
Definition of densityȡ = m/V
Definition of pressureP = F/A
Pressure of a liquidP = ȡgh
Pascal’s principleP 1 = P 2
F 1 /A 1 = F 2 /A 2
Fluid equation of continuityv 1 ȡA 1 = v 2 ȡA 2
v 1 A 1 = v 2 A 2 = R
Bernoulli’s equation