FRICTION EQUIVALENTS OF TAKE-OFFS
IN RECTANGULAR DUCT

BY

LUKE ANTHONY YERKOVICH

 

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1950

THESIS

 

ACKNOWLEDGZENT

The author wishes to express his appreciation for
the assistance received from Power Laboratory technicians
Donald Seble and Carl Redman. He is particularly in—
debted to Professor Lorin G. Miller, Dean of Engineering,
under whose direction the experimental work was conducted.
Similarly Mr. James n. Yohn is to be thanked for his very

helpful COOperation.

{236303 0

Introduction ............................
Equipment ...............................
Orifice Plate Arrangement ...............
Measuring Stations ......................
Orifice Plate Calibrations ..............
Test Procedure ..........................
Determination of Friction Equivalents ...
Discussion ..............................
Conclusion ..............................

Author's Comment ........................

Page No.
l
2 & 3
4
5
6
7 & 8
9
10, ll & 12
13 & 14
15

INTRODUCTICN

It is now generally accepted by those who realize
the friction effect of metal duct work toward air flow
that any change imparted to the air stream will in some
way disturb the flow characteristics of the stream. In
order to determine some of these disturbances this pro—
ject was undertaken under the auspices of the American
Society of Heating and Ventilating Engineers to deter—
mine the friction effect of take—offs in an air
delivery system.

This paper involves a small portion of take-offs
to be tested. Though not representative of any particu-
lar installed system, the subsequent data offers
considerable information on friction effect and air
separation. It is not within the s00pe of these tests
to go into the mechanics of flow, but the paper shall
endeavor to establish a method for determining Optimum

conditions for design and installation.

The assembled equipment, a sketch of which is
illustrated in Fig. l is located in the balcony of
the Power Laboratory, Olds Hall of Engineering. It
is intact for further testing of the remaining fittings
presented in Fig. 2. This equipment consists of a
Clarage blower type W 2 belt driven by a 9.5 horse—
power 440 volt motor. Air discharged by the blower
is forced through a straightener grid prior to its
passage to the measuring nozzle. The nozzle, a 6
inch A. S. M. E. standard long radius nozzle is
equipped with a static tap and pitot tube as outlined
in the A. S. M. E. Power Test Codes, 1940 Chapter 4.
It allows measurements with sufficient accuracy. Mano-
meters employed for measurirg;the velocity pressure at
this nozzle range from 8 inches to 5 inch and are shown
in Fig. 8.“ With the above arrangement this system is
capable of delivering up to 1800 cubic feet of air per
minute.

To b certain that the measured air is passing

(D

through the orifice plate located in the reduced straight
and take-off, all seams and joints in the duct have been
solder sealed. With the system closed off, i. e. in-

serting blanks in the reduced straight and take-off,

-2...

the measured velocity pressure at the nozzle is .002
inches of H20.

In conjunction with the assembled equipment orifice
plates have been cut from 20 gauge galvanized sheet
metal to approximately 25, 50, 75 and 100 feet of
equivalent round duct correSponding to the rectangular

duct into which these orifice plates are inserted.

15” STRAIGHT szcnou WITH
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ORIFICE PLATE ARRANGEMENT

In the take-off and reduced straight, at some
position slightly in excess of 10 diameters from the
increaser type fitting, tracks have been installed.
These tracks make a very convenient method of exchanging
orifice plates to vary the resistance of either straight
or take-off. The duct into which these tracks are in-
serted is itself slotted on one side. Orifice plates
inserted into duct slots are guided in testing position

by the aforementioned tracks.

61/4 X ”/4

man

52 m ..

 

 

 

Orifice plates for insertion into 3" X 8" Duct.

29' of 5.2" round

7" X 2" II

6 X 1%" = 78' of 5.2" round
6 " X IRA" :1 136' of 5. 2" round
6 X l" = 266‘ of 5.2 " round

 

Fig. 4

Orifice plates for insertion into 18" X 8" Duct.

18%" x 6%" = 33' of 13" round
16‘" X 6 " a 51' of 13" round
15;" x 5%" = 82' of 13" round

 

Fig. 5
Orifice plates for insertion into 18" X 8” Duct.

15" X 5" : 146‘ of 13" round
14" X 4" = 365‘ of 13' round

HEASURIEG STATIONS

There are two measuring stations for the system.
Station 1 being employed to measure the air delivery to
the system and Station 2 employed to measure the static
pressures created as a result of the orifice plate in-
sertions. These measuring stations are shown in figures
8 and 9 respectively. The air delivery measuring station,
designated as Station 1 has already been discussed under
section titled Equipment. It accommodates the P3 and P2
readings. P3 refers to the total pressure or impact
pressure measured with a pitot tube while Pg refers to
static pressure in the nozzle at the plane of the pitot
tube.

The static taps P4, P5 and P6 which are included in
measuring station 2 are located in the main, reduced
straight and take-off respectively. Position of P4 is
directly before the increaser type fitting, P5 and P5
are located at approximately 10 equivalent diameters of
their reapective ducts and on the up stream side of the
orifice plates. hanoxeters ranging from 3 inches to
% inch are adequate for static pressure measurements at

this station.

In order to determine the air distribution of the
system, it was first necessary to calibrate the orifice
plates. These orifice plates of which there are nine
are shown in Figs. 3, 4 and 5. Each orifice is identi-
fied according to size and approximate equivalent length
of apprOpriate round.

Calibrations were made against the 8 inch standard
nozzle and appear graphically in Figs. 6 and 7. The
calibration is accomplished by allowing the measured
air to pass through one orifice plate and measuring the
static pressure in this line. This measurement requires
that either the reduced straight or take-off be sealed
during the calibration run.

It was necessary to make calibration runs in dupli-
cate since the system was reversed, i. e. (1) 18» X 8"
reduced straight and 3" X 8" take off and (2) 3" x 8“
reduced straight and 18" X 8" take off. It is interesting
to note that one set of calibration curves serves both

system set-Ups since these curves fall within the limits

of experimental error.

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Fig. 8

Photogranh of measuring station 1 showing 8 and

% inch.manometers. The array of rubber tubing
Shown is connected to the pitot tube (long pro-
jection from duct; and static tap (short pro-
jection from ducx of the standard nozzle. The
flange of the nozzle is visible as a ring around
the duct in right center of photozraph. Station
accommodates P - P3 measurement (velocity pressure)
to determine vglume of air delivered to system.

 

 

 

Fig. 9

Photograph of measuring station 2 showing 3, 1
and % inch manOmeters. Rubber rubing shown
connected to static tap in main, reduced main
and take-off. Station accommodates P4, P5 and
P6 measurement (static pressures).

TEST PROCEED 3

Testing is performed to determine the resistance
created by the take off and reduction of straight in
the arrangement as illustrated in Figs. 10 and 11. The
determination is assisted by varying the resistance of
the take-off and reduced straight through the insertion
of the calibrated orifice plates. In all, there are a
series of 20 determinations of interchanging orifice
plates.

For known quantities of air delivered to the system,
measured at measuring station 1 as velocity pressure
(difference of total pressure and static pressure
designated P3 - P2) static pressure readings are taken
at station 2. These static pressures, designated P4,

P5 and P3 have previously been described. Having
measured them, the quantities of air passing through

the orifice plates can be determined from the orifice
calibration curves and these quantities used to compute
the velocity pressures in the plane of the static taps.
The total pressures are computed as the sum of the static

and velocity pressures and are designated TP4, TP5 and

The total pressure calculations are made from the

following equations:

Q

4005 : Constant for standard air

l
4005 h2A where Q = volume of air cu ft/min

A = Cross section of duct in ft2

h : Velocity pressure of air flowing through duct

In the above equation h is the unknown which is
solved very conveniently by the nomograph in Fig. 18.

Then:

T? - SP + VP where:

TP Tota pressure at the plane of tap

SP : Static pressure direct reading
VP = Velocity pressure as computed by ntmngraph
Since the air is a static pressure tap immediately be-

fore the air is expanded in the increaser type fitting,
the total pressure must be determined at that plane. The
difference in total pressures of plane P4 to plane P5
and plane P4 to P6 can then be used to evaluate the
resistances of the take-off and reduced straight. Each

portion however must be determined by separate evaluation.

 

 

 

 

 

 

 

 

Fig. 10

System set up for runs 10 through 29 showing 3" x 8"
take off, 18" x 8" reduced straight, and increaser
type fitting. P4 static tap is shown in lOwer center

of photograph.

 

 

 

Fig. 11

System set up for runs 39 through 58 showing
18" x 8" take-off, 3" x 8" reduced straight and
increaser type fitting.

DETERLIHATION CF FRICT Ch EQUIVALEK 8

Friction equivalents of take-off and reduced straight
have been determined by plotting curves from the computed
data. These curves are plotted as total pressure
difference against cu ft/min delivery and appear as a
series of four to a set to represent the inter-changing
of orifice plates in the 3" X 8" duct while the orifice
plate in the 18" X 8" duct is kept constant. These
curves are then compared for the apprOpriate equivalent
round with the friction chart from the A. S. H. V. E.

Guide, an enlargement of which appears in Fig. 13.

 

 

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The inserted orifice plate can be classified as

serving two specific purposes:
(1) A method for measuring quantities of air delivered
through the duct in question.
(2) A method of simulating changes in length of the

duct, thereby varying the resistance of the

system.

The method of measuring has already been discussed.
The data evaluations present evidence that these orifice
plate measurements are consistently accurate. In the
graphical representations of Total Pressure drOp vs cubic
ft/min deliveries, it is observed that the points do not
lie completely on the average curve. This discrepancy
probably can best be accounted for as a result of bulging
of the duct (created by static pressure); in which case
the cross sectional area of the duct changes. Apparently
an affect of the bulging type does exist since a compari-
son of the curves for the 3” X 8" duct with the 18" X 8"
duct shows the latter to present more variance. Conse—
quently, we can assume that the static pressure measurements
are accurate and the calculated velocity pressure in
error.

In varying the resistance of the system by orifice

- 10 _

plate insertions, we were able to simulate a condi~
tion of varying the length of the take-off and reduced
straight and treat the system as one of varying the
length of duct. Again graphic r presentations of
total pressure drOp vs cubic ft/min delivery appear to
justify this conclusion. These parabolic curves follow
the same general shape for 5.2" rounds and 13" rounds
of the A. S. H. V. E. friction flow chart.

The curve evaluations are presented numerically
in Tables 1 and 2 and graphically in Figures 14 and 15.
It is to be noted that the plots of columns 7 against 5
for the 3" X 8" duct appear to be parabolic regardless
of the fact that the 3" X 8" duct is the take~off in one
and the reduced straight in the other. These curves
show that the 3" X 8" duct offers positive resistance
to flow in either system set up, but that this resistance
to flow is larger by approximately 3% widths when acting
as take-off under the best flow conditions. The plots of
column 9 against 5 for the 18" X 8" duct appear widely
scattered. However, it is to be noted that the differ-
ence in any one set is in the vicinity of 1% widths
from the average curve represented as straight lines.
It is believed that the friction effect of the 18" X 8"
duct remains approximately constant for any particular

system set up but changes as the system set up is altered.

-11..

As is shown on the graph, resistance changes from a
negative value for 18" X 8" duct as reduced straight
to a positive resistance for the same duct as a take-off.
The parabolic representation of equivalent length
against Column 5 of tacles I and II indicates that
Optimum flow conditions exist with the ratio of Column
5, approaching 1. Below and above this value, the curves
bend to the right, which indicate increase in resistance.
From a fluid flow standpoint, it might be argued that
the reduced straight for values below 1 is robbing a
portion of the air which normally would be in the plane
of the take-off. On the other hand when the valve is
above 1, the behavior is directly Opposite; the take-
off is robbing air which normally would be in the plane of
the reduced straight. If we consider this interpretation
as being accurate, then.ahen the value of Column 5,
approaches L both take-off and reduced straight deliver
air which lies in their respective planes. We might say
that neither contraction nor expansion of the air at the

entrance of the take-off or reduced straight exist.

CONCLUSION

From the data iresented in this paper we may draw

'the following conclusions:

(1) For the system set ups described, more accuracy in

(2)

(3)

measuring exists in the 3" X 8" duct than in the

18“ X 8" duct. This is shown by the smoothness of

the total pressure drOp vs cu ft/min curves for both
types. The bulging affect in the 18" X 8“ duct may
be the controlling factor of accuracy.

More resistance is developed by the take—off than in
the reduced straight. In cases where the take—off

is small such as a 3" X 8", the resistance remains
positive, but is reduced by a matter of 3% widths

at Optimum flow conditions when changing from take-
off to reduced straight.

When the take-off becomes large, as in the case of

the 18" X 8" duct, the resistance decreases from a
positive value for the duct as take-off to a negative
value for the duct as reduced straight.

Optimum flow conditions appear to exist when the ratio
of % air through small divided by the % ratio of small
area to main is l. The general shape of the equivalent
length curves seem to bear this out. At this condi-
tion of flow it is believed that neither expansion

nor compression of the air exists in the plane of the
- 13 -

separation.

It is obvious from a study of this paper that there
yet remains a great deal of work to be done in this field.
There are many phases such as flow mechanics, orifice
coefficients, air separation and distribution which demand
exploration. The data presented in the paper are based
on limited research, though a great deal of effort has
been put forth to obtain a high degree of accuracy in
the results. It is the hope of the author that this
information may not only be of practical value to
designers and installers, but also that it may stimulate

further investigation by others so that all concerned

will benefit by such research in the forthcoming years.

- 14 _

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Fig. 15

AUTHOR'S COEHENTS

All calculations in this paper are based on
standard air conditions though these conditions never
existed. Nor has there been any attempt to correct
values to standard air values. However, the author
feels that the evaluation as a direct result of these
data obtained is within the limits of monometer and

human accuracy.

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY

MICHIGAN STATE COLLEGE
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NUT-232

MECHANICAL ENGINEERING LABORATORY
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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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HUT-232

Sheet No.

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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Remarks:

 

 

nut-232 Sheet No.

 

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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NUT-232 Sheet No, ’I I

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
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MECHANICAL ENGINEERING LABORATORY
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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
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MECHANICAL ENGINEERING LABORATORY

MICHIGAN STATE COLLEGE

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MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

 

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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“LIT-232

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

RMMMde /f:/ac Inga“?

W’7 (07" I/A/"Xf‘QWM’C—am

 

 

 

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"LIT-232

Sheet No. Q

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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“LIT-232

SheetNo.

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MLIT-232

SheetNo.

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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MLIT-232

MECHANICAL ENGINEERING LABORATORY

Running Log of

MICHIGAN STATE COLLEGE

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MLIT-232

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

 

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MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

 

 

 

 

 

 

 

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MLlT-232

Sheet No.

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

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