Fluid Mechanics Formula Sheet

5/20/2018 Fluid Mechanics Formula Sheet

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FLUID MECHANICS FORMULA SHEET

FLUID PROPERTIES

water= 1000 kg/m3 air= 1.23 kg/m

3 mercury= 13600 kg/m

3 = g g = 9.81 m/s2

PHYSICAL PROPERTIES

Newtons Lawof Viscosity

Cai!!a"y Risein Ci"c#!a"

T#$es

%#!& Mo'#!#s ofE!asticity

Co("essi$i!ity

=du

dy ( / ) =

hr

=2

cos

=

=

/d

dp

/d

dpE

0

vK

d

dp

d

dp=

=

1 1

HYDROSTATICS

P"ess#"eDist"i$#tion

Hy'"ostatic Fo"ceon a P!ane S#"face

Point ofA!ication of FR

%#oyancyFo"ce

P = h FR = PcAxR=xc+Ixyc/ycAyR=yc+Ixc/ycA

FB = f sub

3

sphere r3

4=

hr31 2

c!e =

"

a# $y

# $

y

%

# $y

# 4%/&3'

%

#

4%/&3'

Rectangle Triangle Circle Semicircle Quarter

circle

( "a a"/2 % 2 % 2/2 % 2/4

)$c &"a3'/12 "a3/36 % 4/

4

0.1098%4 0.0*488%4

)yc &a"3'/12 % 4/

4

0.392+%4 0.0*488%4

)$yc 0 "a2&", 0 0 ,0.0164+% 4

a

"

d

a/3

&"-d'/3

4%/&3'


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)INEMATICS

Position Vecto" Ve!ocity Acce!e"ation Vo"ticity

r xi yj zk= + + ui !j "k

r

#= + + =

$

%

%#

# = = +

( ) = ( )x

E*#ation ofPat+!ine

E*#ation ofSt"ea(!ine

De! Oe"ato" Vo!#(et"icDi!atation Rate

dx

u

dy

!

dz

"d#= = = dt

ds

w

d

v

dy

u

d$=== k

/0

yi

$

+

+

=

1

d

d#

( )=

Change Equation

eect a! euati! t sve r a diere!t u!k!w!

ve r w rate

ve r w area

ve r w vecity

5here

= w rate

( = w area

v = w vecity
http://www.ajdesigner.com/phpcontinuity/fluid_mechanics_continuity_equation_flow_velocity.phphttp://www.ajdesigner.com/phpcontinuity/fluid_mechanics_continuity_equation_flow_area.phphttp://www.ajdesigner.com/phpcontinuity/fluid_mechanics_continuity_equation_flow_rate.php


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Note Bernoulli Equation Assumes:

1. w is streami!e

2. steady state w

3. i!viscid uid4. i!cmpressi"e uid

eect a! euati! t sve r a diere!t u!k!w!

ve r head ss

ve r static head r eevati! at pi!t 1

ve r pressure at pi!t 1

ve r vecity at pi!t 1

5here

h = head ss7 = static head r eevati!

= ressure

= uid vecity

p = uid de!sity

g = acceerati! gravity

= w rate
http://www.ajdesigner.com/phpbernoulli/bernoulli_theorem_equation_velocity_v1.phphttp://www.ajdesigner.com/phpbernoulli/bernoulli_theorem_equation_pressure_p1.phphttp://www.ajdesigner.com/phpbernoulli/bernoulli_theorem_equation_static_head_elevation_z1.phphttp://www.ajdesigner.com/phpbernoulli/bernoulli_theorem_equation_head_loss.php


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Quantity Symbol Object Units

pressure p scalar N/m2

velocity v vector m/s

density scalar kg/m3

viscosity

scalar kg/m-sbody force b vector N/kg

time t scalar s

barotropic A barotropic fluid is one whose pressure and density are related

by an equation of state that does not contain the temperature asa dependent variable. athematically! the equation of state can

be e"pressed asp#p$% or # $p%.

compressible A fluid flow is compressible if its density changes appreciably

$typically by a few percent% within the domain of interest.&ypically! this will occur when the fluid velocity e"ceeds ach '.3.

(ence! low velocity flows $both gas and liquids% behaveincompressibly.

density, &he mass of fluid per unit volume. )or a compressible fluid flow!the density can vary from place to place.

incompressible An incompressible fluid is one whose density is constanteverywhere. All fluids behave incompressibly $to within *+% when

their ma"imum velocities are below ach '.3.

inviscid Not viscous.

irrotational An irrotational fluid flow is one whose streamlines never loop backon themselves. &ypically! only inviscid fluids can be irrotational. ,f

course! a uniform viscid fluid flow without boundaries is alsoirrotational! but this is a special $and boring% case.

laminar(non-

turbulent)

An organied flow field that can be described with streamlines. norder for laminar flow to be permissible! the viscous stresses must

dominate over the fluid inertia stresses.

Mach ach number is the relative velocity of a fluid compared to its

sonic velocity. ach numbers less than 0 correspond to sub-sonicvelocities! and ach numbers 1 0 correspond to super-sonic

velocities.

Newtonian A Newtonian fluid is a viscous fluid whose shear stresses are a

linear function of the fluid strain rate. athematically! this can be

e"pressed as ij# KijqpDpq! where ijis the shear stress

component! and Dpqare fluid strain rate components.

perect A perfect fluid is defined as a fluid with ero viscosity $i.e.

inviscid%.


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rotational A rotational fluid flow can contain streamlines that loop back on

themselves. (ence! fluid particles following such streamlines will

travel along closed paths. 4ounded $and hence nonuniform%viscous fluids e"hibit rotational flow! typically within their

boundary layers. 5ince all real fluids are viscous to some amount!

all real fluids e"hibit a level of rotational flow somewhere in theirdomain. 6egions of rotational flow correspond to the regions of

viscous losses in a fluid. nviscid fluid flows can also be rotational!but these are special nonphysical cases. )or an inviscid fluid flow

to be rotational! it must be set up that way by initial conditions.&he amount of rotation $called the velocity circulation% in an

inviscid fluid flow is conserved! provided that the fluid is alsobarotropic and sub7ect only to conservative body forces. &his

conservation is known as Kelvin's Theoremof constant circulation.

Sto!esian A 5tokesian $or non-Newtonian% fluid is a viscous fluid whose

shear stresses are a non-linear function of the fluid strain rate.

streamline A path in a steady flow field along which a given fluid particletravels.

turbulent A flow field that cannot be described with streamlines in the

absolute sense. (owever! time-averaged streamlines can bedefined to describe the average behavior of the flow. n turbulent

flow! the inertia stresses dominate over the viscous stresses!leading to small-scale chaotic behavior in the fluid motion.

viscosity, A fluid property that relates the magnitude of fluid shear stressesto the fluid strain rate! or more simply! to the spatial rate of

change in the fluid velocity field. athematically! this is e"pressed

as # $dV/dy%! where is the shear stress in the same

direction as the fluid velocity V! and yis a direction perpendicularto the fluid velocity direction.

Fluid Mechanics Formula Sheet

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