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RELATION BETWEVT TI“? VELOCITY AND

EIWD PVESBVRYS

A Thesis Submitted to
The Faculty of

VICHIT£E S“ATF COLLEfiE
of

AGRICULTUET '37 APPLIFD SCITfiCE

BY

: a

Robert m. Prench

Candidate for the Dewree of

Bachelor of Science

June 1931

 

 

WHESIS

ACKUOVLTDi“EnT

The author wiahes to firatefullv“ac“nowleuze
the assistanco which has lecé received from
Professor C. L. Allen of the Civil Enfinecr—
in; ucpartnent, Michifan State Colle 9, under
whase general cirectiun this stacv and thesis
have been completed. A130 to thank “r. E. A.
Finnev of the Civil Enginecring dcnsrtnent,
?1chifan State Collere, for many helpful sug-

gestions and the uge of necessary ancaratun.

9411.6

V"‘\'.'T"“."T "‘1'???"
"“‘-4‘.’~‘<14JA“ _‘ 'II"

V-—-Velocity of ri-fl in 1.P.U. of air hittine plate.
V1—-Hanoneter reading.

Vt—-Avera:e Velocity for entire Tunnel.
P—--Pressure of wind in oounds per square inch.
P1--Cra s on balance.

D—-—Eensity of Fedium.

K--C9nstnnt.

)

w---Tei*ht of Air hittinr Plate.

w-—-:ei;ht of air in poun e per square foot.
H—--Preseure heed.

a—--C:oss-secticn ar*a of air stream.
E---iase of air at weight w.
g---Acceleration due tn Trevity.

Foo—Force exerted by air on Plate.

C---Velocity coefficient for plate.

Because the modern tall buildins frame constitutes
one of the most indeterminate structures in common use,
in regard to wind stresses, it is of utmost ieoortance to
determine a prooer uniform wind pressure and its distrib-
ution over the surface exonsed. These facts are not sen-
erally_reco“nized because the very tall buildinq in which
wind stresses are of rajor imnortance is of comparatively
recent orifin, and because the maxim n forces ( ind storms)
for which they must be desi nee are OI rare occurrence,
and therefore, the structu e inadequately desifned for wind
may serve for many years withzut rivinr any indic tion of
weakness.

There is a present d<y aritation favorin* the increas—
in- of the allowable norkinr stresses used in the desifin
of structural steel. This is based on the assumotion that
the actual stresses which will exist in the structure can
be calculated within reasonable limits, sue to the feet
that steel structures, such as tall build n's, are so in-
determinate as far as stresses oroduced by mind are con-
cerned, that the win‘ wind velocities and resultinc press-
ures are only nporoxinations: As the hei’ht of these
structures incresses, these stresses become of major im-
portance, *ni the determination of the orooer uniform wind
pressure is inner'tive.

The wind velocities ouhlished by the United 5tatss

Weather ?ureau are indiccted velocities on the standard

L0

four-cup anenometer, and the three—cup anemometer. The
four-cup anenoeeter has an indicated velocity which is
about 20 per cent hish. However, the three—cud anenometer

which has been sed recently sives very accurate readinss.

(I;

Recause durinr tornadoes an hurriesnes the instru-
ments that are set to we sure the velocities are destroyed
by the storrs that they are to measure, it is not known
what the exact velocities the wind may attain. The fol-
losinr is taken from the Vonthly Weather Review, January
1883:
”Summit of Ft. Washincton, N.H., Jan. 3,.1883.
The wind incrensed to a violent hurricane, breaking
off the anerometer at the dial. At the time the inn
strument was broken, a velocity of 152 mi. per hour
was refistered. .It was iniossitle tw reclace the
anenomcter durin the violence of the storm. In order
to measure the rain fell, the observer Wus compelled
to crawl to the rain guess, it beén“ impossitle to
stand b fore the fcrce of the wind. The storn con-

tinued durin': the 4th.“

From the Bulletin of the America: "eteoroloxical

Society, Decenber, 1335, the followinr is taken:

"On February 23, 1896, the mean hourly velocity
(at the summit of Ft. mashinrton) ior 24 hours was
111 miles oer hour, and in January, 1Q78, he extra—

ordinary velocity of 183 miles per hour occurred."

3.

Durinr the Yieni hurricsne no satisfactory recor s
were secured cue to the f ct th"t the e oaretus of the
weather Bureau was located on a low builiinr surrounded
“y tall buildin s. The observer estimated the velocity
to hive been between 113 and 123 wiles per hour. An enem—
oneter at Allisgn Fosiitel, on ”is i chch, onlv e few
miles away was blown down with the maximum velocity re-
corded as 128 niles per hour.

Some of the hiyh wind velocities on record are as

follows:

130 H.P.H. Got. 18, 1916, Pensacola, ?13.
130 “ ” ” Sect. 8, 1900, “alveston, Tex.
(Aneroneter was blown down).
120 " ' " Aur. 7, 1999, San Juan, P.R.
115 n " ~ not. is, 1915, "obile, Ala.

’7’
i)
01
a
a
3

Aug. 20, 1904, St. deul, ”inn.

93 ” ' ' Feb. 33, 1713, New York
98 " u “ De . 33, 1933, Duffelo, H. .

Eeny other velocities exceedinv 93 T1193 per hour

a
‘P

have been recorded in different per.3 o- the Wnited States.
These are the true velocities as the indicate! velocities
would appear to be 130 to 133 tiles per haur. At tires
the extreme velocities up to 159 miles per hour mirht oc-
cesidnslly occur.

Wind pressures on large surfaces is usually less per
unit area than on swell surfaces. This is due to the

gusty nature of the wind end also to the fact that the wind

acts as a shaft or stree~ of sir in entice rather than as

4.

the body as a wh-le mDVlnr s11 s rts with the sewe velocity.
Hr. R. Fleming state: in "fiini t=‘or“111.7515; “dfi Their Vxneri-

mental Basis“ :

”On twe Fortfi erd“0 two orcssure Duaras were set

(‘9'
o
H)
’1
O
.3

up, one 33 ft. lon: and 13 ft. hijh, and R f
it a circular plate 1: sq. ft. in area. The waximum
pressure reristered on the s:ail plate ‘urinr the years
1884 to 1890 W?8 41 lbs. per sq. ft. The 15??? board
shared at the save time a pressure of 37 lbs. per sq.
ft. The readines for the leer. board never exceeded
80 per cent of those recorded on the snail plate at the

sage time, en” fenerally were 59 t? 73 Per cent~"

The sa'e thin? was noted C7 *r. Julius Fairs in the St.
Louis tornsoo of Ray 2?, 1978. isrt of the approach of the
Eads Eridre was dare ed r“grin” the stars, and Fr. Fnirc cel-
culated from the serent of stcbility, the overturninq force
exerteu by the wine, also f7? a brick chirnev and a resin

elevator which was 13 feet hirh, end 200 feet lone. In

his canclusions he states the followinrz

IIt fcve evidcnce thet wind nressure existed at
lesst equivalegt to or trester than 83'1bs., 80 lbs.
and 85 to 90 lbs. per sq. ft., over 0 nsiierable

areas. “hatever the actual distribution may have

been, the effects were those of ssch pvesssres uni—

formly distributed over the arses of the respective
structures. These pressures were measured by their
results in exactly the es‘e manner in which they are
ordinarily assumed to act, with the consequent elim-
ination of all uncertainties usually involved in
readinfs of pressure snares or deductions from an-
emoeeter records, and the are to th"t extent posi-

tive and definite.“

From this evidence it woul’ he safe to rive some re-
duction to the unifor: pressure es the area exposed incre—
ases. A copy 0’ the curve in which 3.. Peire plots the onl-
Culeted pressures sreinst their respective arees is given
with this discussion. (Firure II).

According to the “ectonic Theory, V veries as P , or
P Veries as dv3, as stated in ;ir Isaac Teston's fr’st
masterpiece, "Philosophia Naturalis Princioia "atheistica',
the revised edition, Pook II, Section VIII, Prop. XLVIII.
The velocities of pulses propagated in an elastic fluid are
in a ration co:?oundefi of the suhduolicrte ratio of the
elastic “orce directly, and the subduplicate ratio of the
density inversely, supposinf the elastic force 0" the
fluid to be proportional to its condensetionfj er in other
words:

9
V varies as g. , or P varies as dV”.
D

Densitv 0‘ air is so nest a consteut tVnt it may be

considered such for all practical parooses. ¥once, wv have

the e.ustion:

.L)

P ; EVE
The host difficult oert of usin“ this equation For practical
calculations lies in determininr the constnnt (Y). deriving
theoretically from the Newtonic TFeory, we have as follows:
For Air at 3? derrees F. and born etric oressure of

730 mm.

23
i

.0807 lbs,/ cu. ft.

*0
2-:
w :r

n
oars:

. v3 2 .~ocl.sev"3 (v is in fthec.)

22' - 2‘ §

P
Changing (V) to m 1:3 per hour from ft. per sec.:
P

a!

-*43 - oso

wuss:

:_ .0027‘13

Thus we heve as a constant, .C137. Howey r, this is
purely theoretical and is hosed on the assum>tio. that air

is actinf as a liquid.

From the "Desisn and Construction of ”etellic Bridres"

by Hurt and Folk:

. 4

2 t. of' ‘.-“l'." hi‘tin turret
w :_tt. in les./cu. ft.
V z.”elocity in ft./3ec.

a :_Aree or Crosssection of wind stream

Then, W — an
K :_"ass or air 01 wt. 7

g :_ Acceleration due to firevity

 

Thea F - Riv - "'e’v -_-_ wev3
E H
Let a :_ 1 sq. ft.

Replace v by V (miles per hour), we hove:
r ; .0054 v3

This is known es Rsnkine's formula. This has for its
Canstent .0054 which is exactly dout e that of the theor-
etical constant of the Sewtonic Theory and it is readily
seen why there is so such controversey over the correct
value for this constont. The reason for this double value
is that a cushion is forred in front of the plate and a
auction in book of the plate. The first formula does not
take this into consideration.

Sweeton hes exoerimenteo s Treat deal on wind tests
and gives as his formula P _-_- 1/4202) v3. This constcnt
is very near the Newtonic constcnt. Powever, some of the
most careful experiments in recent years rive c:nstents
varyinr tron .0033 to .004 with many values of from .9017
to .007. This tre endous range is due to perheis different
conditions enf instruments of veryin‘ accuracy. ’ne U. 8.
Weather Bureau takes into consideration the effect of hero-
metric pressure and their formula is P :_ .034 8/30 V3,
where B is the barometric reading.

Alon: with the stu y of various formulae of previous

experim nters, a very careful lehOretory study woe wade of

wind pressures and their corresnondinr velocities. The

author was very fertunete in hcvinr 300.39 to 2 wind

tunnel and very scour he velocity ilstrunwnts, unenks to

*1

the renerosity of Pr. E. i. iinnev of the Civil Enrin-
eerinw departmrnt of ”ichiren fitste Collere, she is the
owner of the spnhrstus.

A rod was suspended fro: tr: oivots on too of the
wind tunnel, by thin metal stress. Tn t*is way the rod
was sleeve in a horizontal position as shorn on Plat I.
hasonite plates Vere weds of different known eress and
were mede so that they were interchangeable on the rod,
and always in a plane perpendicular to the rod. hence,
they were in a vertical position.

The forward strep had en ar; extension whiow trans-
ferred the force to the left-hand pen of balance scales.
These lever ares were so constructed that the force on the
plate was transferred t) the scales so that the rrems on
the scales were equal to the total wind pressure on the
plate. A free body diazrss of the forces end Mo-ent arms
are shown on Plato II.

By means of ratinr curves, the total Force on the
plate (in “rvfi8) is converted to lhs./sq. inch, and the
aversve tunnel velocity, (seasured in units on the manom-
eter) to the evera*e velocity on the plate by wultiplyinr
by the constant (C). This in turn is chnn‘ed ti viles per

P
J.

hour by means 0 smother retins curve.
The lauoneter gives the avers e velocity of the entire
tunnel, but the plate is suspended at the center of the

tunnel and the velocity at the center is much hirher then

I - _ I. -L- kb_.~A_.§

l

I

‘ -_. , ~ .7-
v ‘ '
V-_ hH”‘f‘ 4- ‘97-
‘
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.hlwmvb.

the evevere tunnel velocity. To determine the exact re-
lationshio between the averete velocity of the tunnel and
the evereee velocity of the air etrikinr the plate, three
test runs were nede over the surfece of the plate, each at
a different tuqnel velocity. The first test was wade with
a tunnel velocity of 7.8 ?.P.q. fivin“ 3n averare of 13.95
E.P.H. for the air stri‘c;ir1"r the nlete. 9ividinr the plate
velocity by the everere tunnel velocitv rivee the velocity
coefficient for the plete. This coefficient derived from
all teets ”as found to be practically a constant, the av-
erage heinr (1.4003) or practically (1.4). (Qee Takle I)
Xultielyinr he evere e tunnel velocity by this coefficient
rives the correct avera e velocity over the entire plate

which also is equal to the uniform wine load on this sur-

Teets were made on a plate six inches square or one
quarter of a square foot. The velocity enfl correseondinr
pressure were meceured enfl recorded with variations be-
tween 7 m.p.h. end 83 m.p.h. This rivne an averere con-
stant for the formula P :.KV3, of .033514. The average
constant (K) for the first test was .00358 and for the
second test, .003685. The countente for all trials were
between .0033 and .004, meat of the: hein“ verv close to
.0036.

Curv e were plotted with the velocity in U.P.H. as

‘

the abecieez ane the ereseure in lbs./sq. ft. 89 the ord-

Lu

inate. These curves are ver" cleerlv curves of the second

. - ..79
power, txreein“ with tee equation P ;. £v~.

y.- '9.
l

TABUMT 7‘30

7‘ A _ 5 ”Au,"
1 I"1T.£; ' ‘_ -‘.

s‘- r?" W11?

'2; no 777.0711?
TARL? I

Avere e Tunnel
Velocity :_7.8

Average Tunnel
V13 1: 10 mph.
Wen. E.P.H. Yen. T 7 U

)0) .4”.

Diet.

Down
On

Plate

 

 

C O” I 6.4

. 1' 7.8 .
. 8” 9.0 .

3" 10.0

 

. 4” .09 13.6 .13 18.5
. 5” .10 14.2 .16 18.3
7. e" .13 $31.20 3mg
Velocity Totals 73.7 07.8

"Q

‘J..d

Dividin? by 7: 5

“ Av. Vt 1.402

n
O

This rive

tically C 1.4.

To fin? tte evereje velocity on tEe olete,

tunnel velocity (Vt) must he multipliel ty this
The reason for this chnn e in velocities id flue

ction alonf the ides of the tunnel and eleo to

that the tunnel ie 80 constructei that the
air tends t) throw the oath of hi beet velocity

4.

bot.or of the tunnel.

"‘ '7'" n H .
-" O I. ,, . T t ) .‘ :6" .4

 

a constant with no overs e of 1.1333, 0

inertia

10.

1.21

Avereje Tunnel

Vt : 11.1 mph.

‘F'Lfll. afopIHO
Tris?

~‘r,_').

.e45 9.5
.83 11.1

18.8
15.7
18.8
19.7

82:3

2

1’10

\IU.

til'

5

constant (C).

everaie
to the .ri-
the feet

of the

neer the

 

 

TARULATED DATA

TAPL? II

 

 

 

C)

5‘
V1 Vt V v:
”MA 22.1232. V. x a
Hit. v
.03 3.1 8.88 87 3

.03 7.8 10.93 118.0

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TARULAT33 DATA
TAVL? III

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Pal.
1. 19 .17 .?15 5.35 7.u5 51 .33315
3. 30 .365 .33 8.4 9.38 83.1 .F733

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There has been 5 gr‘3t woutvovmrsr eve? tfie effect of
_the slowe of an inclined Surf 08 on the Si?" thrust of the
wind laad, alt ough eany eiperinonts hTVC been tade alon:
those lines. While the pressure on vertiael surfnees is
taken nor ei tn the exposed surface 9 d tfle intensitv is
equal to the essuvei win: oresrare, f7? non-vesticni surfaces
the pressure is 9133 considered to be nornsl to the surface
but of a much iowcr inteuxity, thfit is, for :nfles u) to 80
defrees. Fran sixty defrees to tte vertical wosition, the
intensity is onusidered to be equai t3 tie assumed winfi
preszure.

Cu? of he ?irst accurate tests an: etuioes was wade
on this subject in 1%33 by Tiberue Cevnllo F.¥.3. in his
book votitlei "The Vlewent= of *etural or “rrfricrntrl Phil-

esophy", aqj in thF C??Dter "Of fiir in Votiou Or Cf The

"The forces a? w fluid medium on e fileno cuttinj
the directivn of its motion "iii aiFfe eat 1 clin-

ations V7?191 succee? vely es tko sqner‘s a? the Sines

L!

or these iioiinations.”

This Sane lcw is ierivei Pv *noffori in the "Theor"

of Structures", in the f)11.’)"fi'i‘ manner:

‘

"Let he Wini *e 2331?ed as T; Win' hovifiontnlly
a ainet the surf ce (ab) 0” hei*ht (be) an: evtinr an
aifie (i) "ith the ho?12fintel. L f t‘° 103*t? be one

fdat, Herpenfilowlar t“ tK° 'ian" O? '3“ power. (gee

17.

Let P :.intedeitv we? aim rw foot of the h rizon—
tal wlgfi force on a vertical eurfsce.
P - intensity per sguare foot of mar-e1 wini
force ectier on surface (ab).
Pt :_int~dsity per square foot of the tenrential

force actin“ on surfnee (Pb).

The total horizoatsl pressire

O
r,
{3
” 3
H:
s;
O
(D
$33
0‘
V
Ct
{D
:3

ezusls Ph.

Fhe nwr*el 03"Oi‘ut of this ;r<esure - Ph sin 1

The int gait! of tne mm? :L com.onent - PB sjn
ab
But an :_ __
Sin 1
Therefore: 9
P P sin” 1

- ',.+'.-.°.:-. ',..,~.‘, : .- - ,. -.-°~
aSSRL.Lc€S titcit U.A'\.¥ .'= 111v («1.033 In 8:; Q I‘L23ut J "31:12": “hlcn

" -- .-- - n‘ AA . -‘ 5 ~ - r-r‘ .- ‘- -
30‘7“ V‘iI v Care. L11- (‘X )trrl'?“ (3%.: 39:9 3‘.ch -? ’fOlJn']

:2)
‘1
3
4
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H.
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L1
9
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IDuchenin, a French M'ie his investiqations
in 1829. These were veri”iei by 9 P. Lfn 1ev in IQRS.

1mm“lcy V‘rief only 3 0e? cent with Cuchevin. The result

<>f thei“ stulie: is the formula the“ is caueieerod t3 he
the best ehpiriCél for ule in one tofi y;

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TABLE VI

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FIGURE 11 —— ?*IEI, TYRINEL

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Applied Texnxnaics at FulanM? That}? A ricultth;l Collere,
recoxnenfie usiuf 33 Tounfs per 9 n:?* fist in all building
dcslw

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B [ELIO’Y-YAPTEY

1. 'Wind Forces“—-—Eu;ineorin; “ewe Record, ”arch 33, 1388

Professor F. F. flawley.

8.'Frared Structures ani Giricrs”----”arburq.

3.

”Wind Vormulas and Exoerlmontal Rasis"--—Vnrineerioq

News, January 39, 1915; R. Fleming.

"Tind Pressure 13 the St. Louis Tornado"—--Trans. Ar.

coo. Civil anrs., Vol. 37, Pare 231; Julius Bair.

"Practiool Hesi n of Tiud Bracing”—--Americon Institute

of Steel Construction, Inc.; Clyde T. "orrls.

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