fluid & heat
TRANSCRIPT
Most Awesome Teachers EVAR!!!!
Overview Fluid: A substance that flows
Usually a liquid or a gas
Hydrostatics: the study of a fluid at rest Ex) Pressure at depth
Hydrodynamics: the study of a fluid in motion Ex) Flow rate
Ideal Liquid: Incompressible (so that density does not change)
Maintain a steady flow rate
Non-viscous
Irrotational flow
Hydrostatic Pressure Measure of the pressure a fluid exerts on the walls of
the container
SI Units: Newton per meter squared :
Aka the Pascal
Sometimes measured in atmospheres (atm)
1 atm is the pressure exerted at sea level
1 atm = 1.013 x 105 Pa
2m
N
Hydrostatic Pressure (cont)
p1 is at the surface and is 1 atm To find pressure at depth (p2): p2 is the absolute pressure
the total static pressure at a certain depth in a fluid, including the pressure at the surface of the fluid
Difference in pressure: Gauge pressure: the difference between the static pressure at a certain depth in a fluid and the
pressure at the surface of the fluid
Pressure at any depth does not depend of the shape of the container, only the pressure at some reference level (like the surface) and the vertical distance below that level
h h h
p2 p2 p2
p1 p1
p1
ghpp 12
ghpp 12
Buoyancy Buoyancy is the weight of the displaced fluid
Archimedes’ Principle states that a body wholly or partly immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces
Buoyant Force: the force that pushes the object upwards
Fluid Flow Continuity Flow Rate Continuity: the volume or mass entering
any point must also exit that point
A = Area of the respective tube
V = Fluid speed in the respective pipe
Mass must be conserved, so mass in M1 = M2
A1
A2
v1 v2
Mass flow Rate: pAv
Density of fluid x Area of tube x velocity of fluid in tube
Equation of Continuity: the flow rate through tube 1 is the same as tube 2 so:
1 A1 v1 = 2 A2 v2
Volume flow rate: the density of the fluid is the same throughout the pipe
A1 v1 = A2 v2
A1
A2
v1 v2
Bernoulli’s Principle Bernoulli’s Principle: the total pressure of a fluid along
any tube of flow remains constant
y = height
v = velocity of fluid
If density of the fluid is p then:
y1
y2
v1
v2
2
2
221
2
112
1
2
1gyvpgyvp
Fluid moving through a horizontal pipe (y1 = y2):
This equation implies that the higher the pressure at a point in a fluid, the slower the speed, and vice-versa
Continuity Principle and Bernoulli’s Principle used together to solve for pressure and fluid speed
2
22
2
112
1
2
1vpvp
Part the second of Chris, Baby, and Kevin’s epic PowerPoint series
Mechanical Equivalent of Heat States that heat and motion are virtually
interchangeable and in any circumstance a given amount of work would produce a given amount of heat
1 calorie of heat = 4.1868 joules per calorie
Heat Transfer Heat Transfer: the movement of heat between two
substances, occurs through conduction, convection, and radiation
Conduction: heat transfer as the result of collisions between molecules in a material, or between material Since molecules in a solid are not free to move, this is accomplished through
vibrational kinetic energy
Convection: heat transfer as the result of mass movement of warm material from one region to another
Radiation: energy transfer as the result of electromagnetic waves
Conduction Rate of heat flow through an object, as a result of
conduction
= heat transfer per unit time
A = cross sectional area of an object
= object’s thickness
T = temperature
K = the thermal conductivity of the object
SI unit is kcal/(smC) : C = degrees Celsius
)( 21 TTKA
t
Q
t
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t
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Radiation Stefan-Boltzmann’s Equation: calculates rate at which
an object radiates electromagnetic energy
= rate at which energy leaves the object
A = object’s surface area
T = object’s temperature in Kelvin
e = emissivity of the material
Perfect absorber is also a perfect emitter and e = 1
4ATet
Q
t
Q