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 ReviewFluid

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 ReviewFluid

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 ReviewFluid

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

AhAPR cavg cc

xcR yAy

Iy cc

xycR xAy

Ix

OFree Surface

dF

hhC

A

dA

R

x

y

y

Centroid, c

yc

yR

Center of Pressure, CP

Fluid Forces on SurfacesFE Fluids ReviewFluid

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Reynolds NumberFE Fluids ReviewFluid

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Bernoulli EquationFE Fluids ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Mechanical Energy EquationFE Fluids ReviewFluid

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Minor LossFE Fluids ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

HGL and EGLFE Fluids ReviewFluid

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

22

22

Ls

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Impulse-MomentumFE Fluids ReviewFluid

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 ReviewFluid

Properties

Fluid Statics

Fluid Dynamics

Energy, Friction Loss, and Pipe Flow

Momentum and Drag

Good Luck!!!

Steve BurianDepartment of Civil & Environmental Engineering

burian@eng.utah.edu