Mind Map Gallery Fluid Mechanics Concepts
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Fluid Mechanics Concepts
A complet mind map about fluid mechanics concepts: Fluid at Rest, Fluid in Motion, Pascal Principle, Bernoulli's Principle, Archimedes Principle, etc.
Edited at 2021-02-19 15:01:03
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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 & 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