Fluid Inst Notes

7/30/2019 Fluid Inst Notes

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FE Review Course ManualLesson 9: Fluid Mechanics

Professional Publications, Inc. 9-1

Lesson 9: Fluid Mechanics

Suggestions for Instructor Review Prior to Class

FERM chapters 2225

Overview

Though some students preparing for the FE exam may not have studied fluid mechanics, the

concepts are based on physics and should be accessible with review. Be familiar with the

formulas in the NCEES Handbook, particularly those indicating how to read the Moody friction

factor diagram and drag coefficient tables.

This lecture should follow the Statics lecture, which introduces calculations for moments and

products of inertia.

General Advice

It will prove useful to memorize the following concepts and equations, rather than needing to

look them up in the NCEES Handbook.

Hydrostatics pressure equation

Force magnitude and location due to hydrostatic pressure for horizontal and vertical plane

walls

Conservation of mass

Conservation of energy

Darcy equation

Relative roughness equation

Drag equation

How to use the Moody diagram


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9-1 Definitions

Fluids

Everything is a fluidgas,liquid, even objects we think

of as solid. Granite flows; it

takes eons, but it flows.

For the FE exam, however,

fluids are limited to substances

that cannot support shear

forces.

Density

Mass per unit volume.

Specific Volume

Volume per unit mass, the

inverse of density (1/).

Traditionally, specific volumeis shown as a lower-case

Greek upsilon, ; however,the NCEES Handbook uses an

italic v as a symbol for

velocity (which looks similar

to the Greek upsilon.) The

lower-case Greek nu, , is

used for kinematic viscosity.

The upper-case italic Roman

letter V is used for volume,

velocity of plate on film, and

flow velocity. This makes the

notation a little awkward,

because there is no symbol for

specific volume besides 1/.Specific Weight

Weight per unit volume (g).

Specific Gravity

The ratio of fluid density

compared to a standard

substance, usually pure water.


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Example: Specific gravity

Shear Stress

Normal component: pressureTangential component:

~ Newtons law of viscosity

~ Power law

K= constant index (a

material property)

n = power law index (a

material property)

n < 1 pseudoplastic

n > 1 dilatant

n = 1 Newtonian

Figure: Shear stress behavior of

different types of fluids

Fluids do not necessarily have

to have a linear relationship

(i.e., n = 1) fort.

Other types of fluids:

Bingham, pseudoplastic, and

dilatant.

Safe to assume that Bingham

fluids will not appear on the

FE exam and that problems

dealing with pseudoplastic or

dilatant fluids will be limited

in scope.


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Absolute Viscosity

Ratio of shear stress to rate ofshear deformation.

Can be measured by putting a

liquid in a container with a

hole in it and measuring the

time the liquid takes to drainout of the container. The

longer the time, the greater the

absolute viscosity.

Surface Tension

Force per unit contact length.Resulting from the energy

necessary to create surfaces.

Capillary Rise

Generally, solids have lower

surface energy when in contactwith liquids than with gas.

Thus liquids have an upwards

meniscus at a wall and, in a

narrow tube, the energy

difference is enough to lift an

appreciable column of liquid.

Example: Capillary rise


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9-2 Fluid Statics

Gage and Absolute Pressure

pabsolute =pgage +patmospheric

Hydrostatic Pressure

~ In a static fluid, the pressure is

dependent on the height of the fluidand independent of the surface area

of the fluid (normal to the direction

of gravity). The height of the fluid

is referred to as head.

Example: Fluid statics

Example (continued)

Manometers

Figure: Open manometer

~ h1 is taken in the middle of the

opening because that is the average

pressure.


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Example: Manometers

Barometer

~ A device used for measuring theabsolute atmospheric pressure.

~ Contrary to common belief,

barometers (and mercury

thermometers) do not have a

vacuum above the mercury; that

space is filled with mercury vapor.

Forces on Submerged Surfaces

Example: Forces on submerged

surfaces


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Center of Pressure

The resultant force can beassumed to be directed through

the center of pressure.

The center of pressure is where

the resultant force of the

pressure will act.

The location of the center ofpressure is a function of the

moment and product of inertia

of the surface under pressure.

Note that FERM Fig. 23.9 is

confusing: the figure in NCEES

p. 45 is much better.

Example 1: Center of pressure

Example 1 (continued)


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Example 2: Center of pressure

Archimedes Principle and

BuoyancyA floating body displaces fluid

equal to its weight.

Center of buoyancy is the

centroid of the submerged part.

A body that is less dense thana fluid in which it is

submerged must have a

restraining force equal to the

buoyant force of the part held

submerged, less the body

weight (in air).

A body that is denser than a

fluid in which it is submerged

has a buoyant force equal to

the weight of the fluid

displaced, so the body appears

to weigh less submerged.


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9-3 Fluid Dynamics

Hydraulic Radius for Pipes

~RHis the area divided by the

wetted perimeter.

~ To find the hydraulic radius, use

the area for a circular segment (A),

then find the arc length (s) from theNCEES Handbook.

Rh = A/s

A = (r2(- sin ))

s = 2rarccos (r - d)/r

Example: Hydraulic radius

Note: Caution students on the unit

of the angle should be in radians,

NOT degrees.

Continuity Equation

~ Mass must be conserved in aflow, so the rate at which mass

flows must be conserved as well.

~ If the fluid is incompressible or

the flow is continuous (no

compression change), then 1 = 2;

thus simplify the continuity

equation.

Example: Continuity equation


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Field (Bernoulli) Equation

~ Energy is conserved in a fluid

flow. The Bernoulli equation

represents the energy of the system.

~ The simplest form of the

Bernoulli equation neglects losses

and only includes pressure,potential, and kinetic energies. It is

valid for incompressible fluids

along the same streamline.

Example: Fluid dynamics

Note that in the example as given,the pipe cannot be of constant

cross-section, otherwise the

pressure at 15 m depth would be

negative.

Example (continued)


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Flow of a Real Fluid

~ The Bernoulli equation is

improved by taking the head loss

due to friction into account.

Fluid Flow Distribution

~ The velocity of a fluid flowdepends on how far the fluid is

from the walls of pipe.

Reynolds Number

~ We need the Reynolds number to

find out how turbulent the flow is,

because friction loss in fluids is

less when the flow is turbulent.


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Example: Reynolds number

Hydraulic Gradient

~ Pressure head decreases as afunction of distance traveled

because pressure head is lost due to

friction.

~ The hydraulic gradient is the

decrease in pressure head per unit

length of pipe.

9-4 Head Loss in Conduits

and Pipes

Darcy Equation

~ Since the friction loss is not a

linear relationship, the friction

factorfis used to account for the

nonlinearity.fis a function of the

Reynolds number and relative

roughness (i.e., specific roughness

divided by hydraulic diameter).Figure: Since the friction factor is

not a linear function, it must be

looked up on the Moody (Stanton)

diagram. Its worthwhile taking

lecture time to explain how to read

this chart, which is in the NCEES

Handbook and FERM.


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Minor Losses in Fittings,

Contractions, and Expansions

~ The accuracy of the Bernoulli

equation is improved by taking into

account the loss due to fittings in

the line and contractions or

expansions in the flow area.~ The loss depends on the velocity

of the flow and the characteristics

of the fittings, contractions, or

expansions. These characteristics

are accounted for by a loss

coefficient C.

Explain loss coefficients for

entering and exiting a pipe.

9-5 Pump Power Equation

~ Q is the quantity of flow.~ h is the head increase to be added

to the flow.

9-6 Impulse-Momentum

Principle

~ Sum of forces = rate of

momentum entering minus the rate

of momentum leaving.

Pipe Bends, Enlargements, and

Contractions

~ The force is resolved into itsx

andy components.


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Example: Bends, enlargements,

and contractions

Example (continued)

Example (continued)


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9-7 Impulse-Momentum

Principle

Jet Propulsion

~ The force of the jet from an

orifice on a tank is related to the

energy in the flow. The energy in

the flow is equal to the differencein potential energy between the

surface and the orifice.

Fixed Blades

~ The force is resolved into itsxandy components.

Moving Blades


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Impulse Turbine

~ Figures: Impulse turbine and

turbine power graph

~ Equations: Turbine power

9-8 Multipath Pipelines

The pressure when the pipesseparate and join is the same, so the

head loss is the same. It has to be,

because if one were greater than

the other then the flow would move

back up the other pipe. Since the

pressure is the same, the head loss

is the same regardless of the path.

9-9 Speed of Sound

Speed of sound in a fluid is a

function of its compressibility.

Mach number the ratio of the

objects speed to the speed of

sound in the medium through

which the object is traveling

Example: Speed of sound


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9-10 Fluid Measurements

Pitot Tube

~ A device to measure the velocity

in a flow.

Example: Pitot tube

Venturi Meters

~ A device for measuring the flow

rate in a pipe system.

~ Cv= coefficient of velocity (see

the NCEES Handbook table).


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Example: Venturi meter

Example (continued)

Orifices

~ An orifice meter is analyzed

similarly to a venturi meter.

Cis the meter coefficient,

depending on the orifice opening

(see the NCEES Handbook table).


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Submerged Orifice

~ If the characteristics of a

submerged orifice are known, the

flow rate through the orifice can be

calculated.

Drag Coefficients for Spheres and

Circular Flat Disks~ This chart gives drag coefficients

as a function of Reynolds numbers.

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