Kaplan — Physics & Math Flashcards
Fluid
Have ability to flow and conform to the shapes of their containers
Both liquids and gases
Solid
Does not flow and is rigid enough to retain a shape independent of their containers
Density
Ratio of mass to volume
Specific gravity
Density of a substance over the density of water (1 g/cm^3)
Pressure
Ratio of force per unit area
Absolute (hydrostatic) pressure
Total pressure that is exerted on an object that is submerged in a fluid
Absolute pressure formula
P = P_0 + rho x g x z
P_0 → incident or ambient pressure (pressure @ the surface)
Rho → density
g → gravitational acceleration
z → depth of object
Gauge pressure
Difference between the absolute pressure and the atmospheric pressure
Hydrostatics
Study of fluids at rest and forces & pressures associated with standing fluids
Pascal’s principle
For incompressible fluids, a change in pressure will be transmitted undiminished to every portion fo the fluid and to the walls of the containing vessel
Hydraulic system relationships
If pressure is the same:
F_2 = A_2 * F_1 / A_1
F_1 * d_1 = F_2 * d_2
Archimedes’ principle
F_buoy = rho_fluid * V_fluid displaced * g = rho_fluid * V_fluid submerged * g
Surface tension
Causes the liquid to form a thin but strong layer like “skin” at liquid’s surface
Cohesion
Attractive force that a molecule feels toward other molecules of the same liquid
Adhesion
Attractive force that a molecule of the liquid feels toward the molecules of some other substance
Meniscus
Curved surface in which liquid “crawls” up the side of the container a small amount
Adhesion > cohesion
Convex meniscus
Inverted form of meniscus
Adhesion < cohesion
Fluid dynamics
Study of fluids in motion
Viscosity
Resistance of fluid to flow
Viscous drag
Non-conservative force that is analogous to air resistance
Inviscid
Fluids with no viscosity
Laminar flow
Smooth orderly flow
Poiseuille’s law
Q = pi * r^4 * delta P / (8 * eta * L)
Turbulent flow
Rough and disorderly
Eddies
Swirls of fluid of varying sizes occurring typically on the downstream side of an obstacle
Critical speed
Turbulence can arise when the speed of the fluid exceeds a certain speed
Boundary layer
Thin layer of fluid where laminar flow occurs
Critical speed equation
v_c = N_r * eta / (rho * D)
N_r → Reynolds number
eta → viscosity
rho → density
D → tube diameter
Reynolds number
Depends on factors such as the size, shape, surface roughness of any objects within the fluids
Streamlines
Representation of the molecular movement
Velocity will always be tangential to streamlines
Continuity equation
Q = v_1 * A_1 = v_2 * A_2
Bernoulli’s equation
P_1 + 0.5 * rho * v_1 ^ 2 + rho * g * h_1 = P_2 + 0.5 * rho * v_2 ^ 2 + rho * g * h_2
Dynamic pressure
Pressure associated with the movement of a fluid
Example: 0.5 * rho * v^2
Energy density
Pressure can be thought of as a ratio of energy per cubic meter
Temperature
Proportional to the average kinetic energy of the particles that make up the substance
Difference in temperature between two objects that determines the direction of heat flow
Heat
Transfer of thermal energy from a hotter object with higher temperature (energy) to a colder object with lower temperature (energy)
Thermal equilibrium
If no net heat flows between two objects in thermal contact
Fahrenheit-Celsius conversion
F = 1.8 x C + 32
Celsius-Kelvin conversion
K = C + 273
Absolute zero
Theoretical temperature at which there is no thermal energy
Third law of thermodynamics
Entropy of a perfectly organized crystal at absolute zero is zero
Zeroth law of thermodynamics
If A = B and B = C, then A = C
System
Portion of the universe that we are interested in observing or manipulating
Surroundings
Rest of the universe
Isolated systems
Not capable of exchanging energy or matter with their surroundings
Total change in internal energy is zero
Closed systems
Capable of exchanging energy but not matter
Open systems
Exchange both matter and energy with the environment
State functions
Thermodynamic properties that are a function of only the current equilibrium state of a system
Independent of the path taken to get to a particular state
Process functions
Path taken to get from one state to another
First law of thermodynamics
An increase in total energy of a system is caused by transferring heat into the system or performing work on the system
U = Q - W
(+) change in internal energy
Increasing temperature
(-) change in internal energy
Decreasing temperature
(+) heat
Heat flows into the system
(-) heat
Heat flows out of the system
(+) work
Work is done by the system (expansion)
(-) work
Work is done on the system (compression)
Universal law of energy conservation
Energy can be neither created nor destroyed; it can only be changed from one form to another
Second law of thermodynamics
Objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature at thermal equilibrium
Heat
Process by which a quantity of energy is transferred between two objects as a result of a difference in temperature
Conduction
Direct transfer of energy from molecule to molecule through molecular collisions — requires direct contact
Convection
Transfer of heat by physical motion of a fluid over a material
Involves flow — only gases and liquids can transfer heat by this means
Radiation
Transfer of energy by electromagnetic waves
Specific heat (c)
Amount of heat energy required to raise one gram of a substance by one degree Celsius
Freezing
Change from liquid to solid
At melting point
Melting
Change from solid to liquid
At melting point
Boiling
Change from liquid to gas
At boiling point
Condensation
Change from gas to liquid
At boiling point
Heat of vaporization
Heat of transformation for boiling and condensation
Heat of fusion
Heat of transformation for freezing and melting
Isothermal process
Constant temperature — no change in internal energy
Q = W
Adiabatic process
No heat exchange
Delta U = -W
Isobaric process
Constant pressure
Isovolumetric (isochoric) process
No change in volume, no work accomplished
Delta U = Q
Entropy
Measure of the spontaneous dispersal of energy at a specific temperature — how much energy is spread out or how widely spread out energy becomes in a process
Second law in terms of entropy
Delta S universe = delta S system + delta S surroundings > 0
Entropy & microstates
As the number of available microstates increases, the potential energy of a molecule is distributed over that larger number of microstates, increasing entropy
