## Fluid Mechanics Concepts

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A complet mind map about fluid mechanics concepts: Fluid at Rest, Fluid in Motion, Pascal Principle, Bernoulli's Principle, Archimedes Principle, etc.

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Fluid Mechanics Concept

Fluid at Rest

Anything that flows

Fluids can be liquid or gas

Solving for Density

Density = m/v; measured in kg/m^3

If an object or fluid is made out of heavier atoms or molecules, then it’s going to have a higher density.

Pressure = F/A; Measured in Pascals (Pa)

Solving for the pressure at a given depth

Pressure = density x gravity x height
Change in Pressure = density x gravity x change in height

Blaise Pascal/ Pascal Principle

The input of your force is doubled on your output.
The bigger difference in area, the more extra force you get.

“If you apply pressure to a confined fluid, the pressure in every part of the fluid increases by that amount.”

Measuring the pressure

Manometers

U shaped tube with a fluid inside

If you measured the difference in fluid height directly, you'd get what's known as gauge pressure.

TO GET THE ABSOLUTE PRESSURE:
P = P0 + density (g) (∆h) gauge pressure P0 = Atmospheric Pressure

Barometers

Long vertical tube filled with mercury. Mercury is used because it is a very dense liquid which means the air pressure supports a much shorter column so barometers can be smaller.

Standard P0 = 76cm

NOTE: If the air pressure goes up, so does the level of the mercury and vice versa.

Fluid in Motion

Low Viscosity

The fluid flows easily, like water.

High Viscosity

The fluids that don't flow as easily, like honey.

Mass Flow Rate

It is always going to be the same everywhere in the pipe.

Equation of Continuity

The mass flow rate at one point in the pipe will be equal to the mass flow rate at any other point.

Δm1/Δt = Δm2/Δt

Bernoulli's Principle

The higher a fluid's velocity is through a pipe, the lower the pressure on the pipe's walls, and vice versa.

Pressure times volume

P + 1/2 p v^2 + pgy = a constant

Kinetic energy density

KE = 1/2 mv^2. Bernoulli divided this form of energy by volume, to get half the fluid's density, times its velocity squared.

Potential energy comes from gravity

So when you look at his equation piece by piece, you can see that Bernoulli was really just putting conservation of energy into a special form that would be useful for fluids.

Torricelli's Theorem

Uses conservation of energy to find the velocity of fluid flowing from a small spout in a container.

The velocity of the fluid coming out of the spout is the same as the velocity of a single droplet of fluid that falls from the height of the surface of the fluid in the container.

The pressure that pushing the fluid out of the spout gives it the same velocity that it would get from the force of gravity.

Archimedes Eureka

Buoyant Force (FB)

Counteracting the force of gravity

Lived in Greece in the third century BCE.

He discovered that when you put something in a fluid, the fluids volume increases by the amount of the object's volume.

Archimedes Principle

There’s a buoyant force pushing upward on object in water, and its equal to the weight of the water that the object displaced.

F_B = m_F g

m_F = mass of displace fluid

King Hieron

sailing vessel, 50x bigger than a standard warship

a gift for Ptolemy (named Syracusia)

Syracusia

-Pitch from France
-Ropes from Spain
-Beams of pine and fir from Mt.Etna

Components

-Ship’s Bow ‘180pound stone missiles
-Top deck 8 towers
-flower lined promenade

-sheltered swimming &amp; bathhouse w/ heated water
-a library
-temple to the goddess Aphrodite
-gymnasium

Problem: Will it sink?

400 tons of grain = 10000 jars of picked fish
74 tons of water
600 tons of wool

It carried a thousand of people w/ 600 soldiers, w/ 20 hours
An object partially immersed in a fluid is buoyed up by a force

FORCE=WEIGHT Of the fluid
2000 tons of water= it barely float
4000 tons of water=it would float
1000 tons of water=it wouldn’t float

Bathtub, explains why a steel can float as easy
Wooden rowboat

Average air pressure at sea level is 101,325 Pa

The water in the pool is one of the examples of a confined fluid.

Members: Mista, Lara Denesse; Narbay, Shanin; Pulido, Abigail; Millanes, Lameye; Reverente, Genevieve 12-STEM