Fundamentals of Engineering (FE) Exam Fluid Mechanics Review Steven Burian Civil & Environmental Engineering March 27, 2015
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Fundamentals of Engineering (FE) Exam
Fluid Mechanics Review
Steven BurianCivil & Environmental Engineering
March 27, 2015
Morning (Fluid Mechanics)A. Flow measurementB. Fluid propertiesC. Fluid staticsD. Energy, impulse, and momentum equationsE. Pipe and other internal flow
7% of FE Morning Session
Up to 15% of FE Afternoon Session
Afternoon (Depends on Discipline)A. Bernoulli equation and mechanical energy balanceB. Hydrostatic pressureC. Dimensionless numbers (e.g., Reynolds Number)D. Laminar and turbulent flowE. Velocity headF. Friction losses (e.g., pipes, valves, fittings)G. Pipe networksH. Compressible and incompressible flowI. Flow measurement (e.g., orifices, Venturi meters)J. Pumps, turbines, and compressorsK. Non-Newtonian flowL. Flow through packed beds
Fluids and FE
Fluids Fluids - substances in liquid or gas
phase
Fluids cannot support shear; they deform continuously to minimize applied shear forces
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Viscosity Shear stress (): force required to slide one
unit area layer of a substance over another Viscosity (): measure of a fluid’s resistance to
flow when acted upon by an external force (i.e., ease with which a fluid pours) As a fluid moves a shear stress is developed
in it; magnitude is dependent on viscosity of fluid
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
F/A is the fluid shear stress () and the constant of proportionality is the absolute viscosity ():
dydu
Newtonian fluids: strains are proportional to the applied shear stress
Non-Newtonian fluids: fluid shear stress can be computed using the power law
The kinematic viscosity is the ratio of the absolute viscosity to mass density:
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Surface Tension “skin” that seems to form on free surface of a
fluid; caused by intermolecular cohesive forces and is known as surface tension, Surface tension - tensile force between two points
a unit distance apart on the surface
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Capillarity Capillary action: caused by surface tension
between liquid and a vertical solid surface Adhesive forces between liquid molecules and
surface > cohesive forces between liquid molecules; in water, adhesive forces cause fluid to attach itself to and climb solid vertical surface
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Pressure
Hydrostatic pressure: pressure of fluid on immersed object or container walls Pressure = force per unit area of surface:
AFP
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Pressure Gage pressure: measured relative to a reference
pressure - typically local atmospheric pressure Absolute pressure: measured relative to a
perfect vacuum Absolute, gage, and atmospheric pressure are
related as follows:
Pabs = Pgage + Patm
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Pressure
Munson et al. (2002)
P1 abs
P1 gage
P2 gage
P2 abs
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Hydrostatic Pressure
P = change in pressure = specific weight of fluidh = change in depth in fluid
P = h
***Incompressible fluid at rest
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Manometry Measure pressure or pressure
differences Differential manometers: both ends
connected to pressure sources Open manometers: one end open
to the atmosphere
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
BarometersFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Buoyancy
Buoyant force = weight of fluid displaced and is directed vertically upward (Archimedes’ Principle):
Fb = Vd
where Fb = buoyant force = specific weight of fluidVd = displaced volume of fluid
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Displaced volume
Displaced VolumeFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
If object at rest in fluid, then use equation of static equilibrium in vertical direction, Fy = 0
Buoyant force passes vertically through centroid of displaced volume; called the center of buoyancy.
Solving Buoyancy ProblemsFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Fluid Forces on Surfaces
Pressure on horizontal plane is uniform over surface
Resultant force of pressure distribution acts through center of pressure of surface and is:
PAR R = resultant vertical forceP = pressure on horizontal surfaceA = area of submerged horizontal surface
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Fluid Forces on SurfacesFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
AhAPR cavg cc
xcR y
AyIy c
c
xycR x
AyI
x
OFree Surface
dF
hhC
A
dA
R
x
y
y
Centroid, c
yc
yR
Center of Pressure, CP
Fluid Forces on SurfacesFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Laminar and Turbulent FlowLaminar Flow: Relatively low velocities No mixing or a very small degree
of mixing Fluid appears to flow in
continuous layers with no interaction between the layers
Relatively high velocities High degree of mixing Fluid motion appears chaotic
Turbulent Flow:
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Flow DistributionFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Reynolds NumberFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Reynolds Number
Re < 2000 laminar flow2000 < Re < 4000 transition regionRe > 4000 turbulent flow
Circular Pipe Flow
Open Channel
Re < 500 laminar flow500 < Re < 2000 transition regionRe > 2000 turbulent flow
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
One-Dimensional FlowsFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Bernoulli EquationFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Mechanical Energy EquationFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Friction Loss
Valid for laminar and turbulent flow
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Moody ChartFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Minor LossFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
HGL and EGLFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
HGL and EGL
Z = 0
Total Head or Energy Grade Line
(EGL)
Elevation Head (z)
Velocity Head (v2/2g)
Pressure Head (P/)
Hydraulic Grade Line
HGL
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Pump-Turbines
g2vzPhh
g2vzP 2
22
2Ls
21
11
Net head added to system by mechanical device
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Open Channel & Pipe FlowFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Impulse-MomentumFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Impulse-Momentum
x111x222x vQvQF
y111y222y vQvQF
z111z222z vQvQF
Sum of the external forces
Net rate of momentum entering control volume
FE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
Pipe NetworksFE Fluids Review
Fluid Properties
Fluid Statics
Fluid Dynamics
Energy, Friction Loss, and Pipe Flow
Momentum and Drag
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