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Chapter 12 OutlineFluid Mechanics
• Density
• Pressure• Gauge pressure
• Pascal’s law
• Buoyancy• Archimedes’ principle
Density,
• Density is the ratio of mass to volume.
• The SI unit for density is , but the cgs unit is also commonly used.
Pressure,
• At rest, a fluid exerts a force perpendicular to any surface in contact with it.
• The unit for pressure is the pascal, .
• Atmospheric pressure is about .
Absolute vs. Gauge Pressure
• When we measure the air pressure in tires, the air pressure gauge might read ().
• For a flat tire, it will read .
• These pressure readings are based on the pressure above the atmospheric pressure, and are called gauge pressures.
• The absolute pressure is the gauge pressure plus the atmospheric pressure.
Pressure and Depth
• Intuitively, we know that pressure increases with depth.
• If you swim down to the bottom of a deep pool, you can feel the increase in pressure.
• Consider an element of fluid at rest.• The forces acting on it are the pressure
from the top, from the bottom, on the sides, and the weight of the element.
• At rest, so the sum of the forces is zero.
Pressure and Depth
• For uniform density,
• Or,
• Where is the surface pressure and is the depth.
Pressure and Depth
• Since the pressure only depends on the depth, the surface of the fluid in a container must be level, regardless of the shape of the container.
Pascal’s Law
• Also, from , we see that if we increase the surface pressure, , that pressure increase is transmitted throughout the entire fluid.
• This is Pascal’s law:
“Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.”
Pressure Example
Hydraulics
• Hydraulics work on this principle.
• A small force is applied to a piston with a small area, and the pressure is transmitted to a large piston and produces a large force.
• Note that the work done does not violate energy conservation.
Buoyancy
• When an object is immersed in water, it seems to weigh less than in air.
• This means that there must be some upward force on the object. We call this the buoyant force.
Archimedes' Principle
“When a body is completely or partially immersed in a fluid the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body”
Buoyancy Example
Chapter 12 SummaryFluid Mechanics
• Density:
• Pressure: • Depth:
• Pascal’s law
• Gauge pressure vs. absolute pressure
• Buoyancy• Archimedes’ principle