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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

Q

t

Q

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