Fluid Mechanics

What is a fluid?

substances that can flow and take the shape of a container rather than retain shape of their own

Are liquids and gasses comprehensible and well defined in shape or volume?

Liquids: typically incompressible, well defined volume but no well defined shape; gases: compressible, no well defined volume or shape

Density

the density of a material (Fluid or not) is defined as mass per volume

Pressure

pressure is defined as force per unit area, where the force F is acting perpendicular to the surface area

Where does pressure in a fluid come from?

From constant random motion of its molecules colliding with each other and the surfaces they encounter

Collision and force

Each collision exerts a tiny force on the wall. The net force due to all the collision causes the gas to have pressure

What does pressure in a fluid depend on?

Pressure depends only on depth/height

Pascal’s Principle

When a change in pressure is applied to an enclosed fluid, it is transmitted undiminished to all portions of the fluid and to the walls of its container

Buoyant Force

The buoyant force is the upward force on any object in any fluid

Archimedes Principle

Any Object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object

What happens if FB is greater than the weight of the object?

the object rises

What happens if FB is less than the weight of the object?

the object sinks

Turbulent Motion

irregular flow characterized by small whirlpool like regions

Laminar motion (Streamline, Steady)

Each particle of the fluid follows a smooth path (paths of different particle never cross each other)

Properties of Ideal Fluids

the fluid density is constant: fluids is incompressible; non-viscous: no internal friction

Properties of Laminar flow

adjacent layers of fluid slide smoothly past each other; flows irrotational: fluid has no angular momentum

Flow Rate Continuity

The volume of fluid passing by a given location through an area during a period of time Q (Q=dv/dt=AV)

How can rate of flow be described by?

By the mass flow rate or mass rate of flows; this is the rate at which a ass of fluid moves past a point (pAV)

Describe flow rate as an incompressible fluid

the flow rate through the pipe is constant: any amount of fluid that passes point 1 in a given time, must also flow past point 2 in the same time (Q1=Q2; A1V1=A2V2)

Fluid moving through a narrow region

The velocity increases, which indicated that there is a net force in the direction of motion of fluid; the Fnet results from change in P in the direction of V P1>P2 where velocity of a fluid is high, the pressure is low, and where velocity is low, pressure is high

Bernoulli’s Equation

The sum of the static pressure, KE per unit volume, and gravitational PE per unit volume has the same value at all points along a streamline