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