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Density
- ρ = m / V
- m: mass
- V: volume
- * remember that density changes with compression because volume will change
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Specific Gravity
- Makes density more intuitive
- SG = ρsubstance / ρwater
- ρwater: 1 g/cm3 or 1000 kg/m3
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Pressure
- P = F / A
- when an object is submerged: pressure is equal to the force felt on the object divided by the surface area
- * remember that pressure is there regardless of if the object is, this just makes it more intuitive
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Fluids at Rest
- Fluids are at rest when they are only experiencing a force perpendicular to its surface
- P = ρgy
- * remember that if the container is open you must add Patmos which is 101 000 Pa
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Pascal's Principal
- Pressure applied to an incompressable fluid will be evenly distributed
- a hydrolic lift utilizes this principal (F applied to smaller S.A. --> P trans --> since the larger S.A. is larger the F is greater on it (no change in work though so the distance is less)
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Archimedes Principal
- an object submerged in water displaces a volume of fluid equal to its own volume
- an object floating displaces a volume of fluid equal to its weight
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Buoyancy Force
- Submerged: Fb = ρfluid V g
- Floating: Fb = mgobj = mgfluid
- Fraction Submerged: ρobj / ρfluid
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Center of Buoyancy
- is the point were the center of mass would be if the object were uniformly dense
- the actual center of the object
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Fluids in Motion - Types of Motion
- 1) Random Translational - contributes to fluid pressure as in a fluid at rest
- 2) Uniform Translational - shared by molecules at a given location
- energy from these two types of motion can be converted back and forth
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How do real fluids compare to ideal fluids?
- real have drag, viscocity
- drag works at the fluid-object interface, therefore the greatest velocity will be at the point farthest from that interface
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Flow Rate
- Q = A v
- Q: volume flow rate
- A: area
- v: velocity
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Bernoulli's Equation
- P + ρgh + 0.5ρv2 = K
- the sum of these three terms is a constant at any point in the fluid
- term 1: pressure
- term 2: potential
- term 3: kinetic
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As velocity increases, pressure
- decreases
- think of the bee swarm standing vs. running analogy
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Surface Tension
- temp dependent - the higher the temp the weaker the surface tension
- if the adhesive forces (to the container) are stronger than the cohesive forces (between molecules) the miniscus will be a 'U' shape
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Solids and Heat
Typically expand when heated
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