PTC-56-2

A ir F low in Fan-D ischarge D uctsB y LIONEL S. M ARKS,1 CAM BRIDGE, MASS.

T h is paper is concerned w ith a n exam in ation o f p ossib le cau ses o f the d iscrepancies which are so m etim es fou n d b e ­tw een p ito t-tu b e m easu rem en ts an d nozzle m e asu rem en ts o f th e volum e o f a ir flowing in a fan -d isch arge du ct. A m ong the conclusion s reached are th e follow ing: (1) Air p u lsa tion s m ay cau se a sm a ll error; (2) In correct lo ca ­tion o f the ou term ost p ito t-tu b e sta tio n re su lts in a n error o f a t least 0.6 per cen t; (3) p ito t-tu b e errors an d non-axial

flow are the prin cipal sources o f error.T h is paper a lso gives th e ch aracteristics o f variou s p ito t

tu bes, shows th a t n on-axial flow ex ists in th e d isch arge from sin gle-in let-cen trifu gal an d propeller-type fa n s an d in d icates th a t th is d iscrepancy can be e lim in ated by th e use o f egg-crate stra igh ten ers w hich it recom m en ds for adoption in stan d ard te s t p ractise . I t is in d icated , too, th a t th e p resen t stan d ard len g th o f te s t d isch arge d u ct can be halved w ithout lo ss o f accuracy an d th e fric tion coefficient om itted .

I t is recom m ended by th e au th o r, a s a re su lt o f th e stu d y covered by th is paper, th a t for te s t purp oses th e term “ velocity head” sh ou ld be redefined an d th a t a m ore p re ­cise specification for th e p ito t tu b e sh ou ld be adopted .

IT HAS BEEN well established that the pitot-tube-traverse method of measuring the volume of air flowing along a fan- discharge duct gives results which may be considerably in

error. Hagen2 has published a table of comparison of volumes, measured simultaneously by pitot tube and by nozzle, and shows that whenever there is a discrepancy between the two measure­ments the pitot tube yields the high value and that the discrep­ancy may be as much as 18 per cent. He suggested that velocity pulsations might be responsible for the discrepancy and pre­sented records from a vibrograph showing the frequency and amplitude of air pulsations in certain ducts. Further work along the same lines in the Gordon McKay Laboratory of the Harvard Engineering School with instruments of greater precision indicates that such pulsations actually occur but, so far as the observations of the author extend, they appear to be of small amplitude and of numerous and varying frequencies. It seems

1 Professor of Mechanical Engineering, Harvard University.Mem. A.S.M .E. Professor Marks was born in Birmingham, Eng­land. He received the degree of B.Sc. from the University of London in 1892 and M .M .E. from Cornell University in 1894. H e was with the Ames Iron Works, Oswego, N. Y. in 1894 and then went to Har­vard University as instructor in mechanical engineering. In 1900 he was made assistant professor and in 1909 was advanced to his present position. Professor Marks is author of “Steam Tables and Dia­grams,” “Gas and Oil Engines,” “Mechanical Engineers’ Handbook,” “The Airplane Engine,” and has contributed numerous articles to the technical press.

* “Pulsation of Air Flow From Fans and Its Effect on Test Pro­cedure,” by Hagen, A.S.M .E. Trans., vol. 55,1933, paper FSP-55-7.

Contributed by Power Test Code Committee No. 10 on Centrifugal and Turbo-Compressors and B I o w c t s for presentation at the AnnualMeeting, New York, N . Y ., December 3 to 7, 1934, of T h e A m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e e s .

Discussion of this paper should be addressed to the Secretary, A.S.M .E., 29 W est 39th Street, New York, N . Y ., and will be accepted until January 10, 1935, for publication in a later issue of Transac­tions.

N o t e : Statements and opinions advanced in papers are to be understood as individual expressions of their authors, and not those of the Society.

For the outer fifth of the cross-section the mean velocity is 0.631 times the center-line velocity. The velocity measured a t the standard distance of 0.949 R from the center is 0.6545 times the center-line velocity. The error due to the use of the standard location in the outer fifth of the cross-section is 1/5(0.6545 — 0.631) X 60/49 = 0.006 or six-tenths of one per cent.

An examination of velocity-distribution curves obtained by traverses of fan-discharge ducts shows tha t the seventh-root law does not apply except near the boundaries. For other than the outermost annular zone the velocity changes are gradual and the assumption th a t the velocity a t the standard location is the cor­rect mean velocity will not lead to appreciable error. The seventh-root law is usually correct in ducts 30 in. or larger in diameter and for the usual range of velocities, for a distance of about 2 in. from the boundary. Consequently, it m ay be con­cluded tha t with 10-point traverses the A.S.H.&V.E. standard test procedure will give results about 0.6 per cent too high and tha t this error can be eliminated by locating the outermost pitot- tube station a t the place giving the correct mean velocity. This

8 “The Physics of Solids andFluids,” by Ewald, Poschl, and Prandtl, p. 281.

871

to the author very improbable th a t such pulsations can account for more than a small fraction of the observed discrepancies.

The possible sources of error, in addition to pulsation, appear to be:

(1) Errors in the A.S.H.&V.E. standard test method(2) Errors in the p itot tube(3) Non-axial flow of the air.

E r r o r s i n t h e S t a n d a r d T e s t M e t h o dW ith round ducts, the A.S.H.&V.E. Standard Test Code pre­

scribes not less than 20 pitot-tube readings (not less than two traverses, of 10 readings each, along perpendicular diameters) a t the centers of areas of five equal concentric areas comprising the section of the duct. The pitot-tube locations are thereby fixed a t distances 0.316, 0.548, 0.707, 0.837, and 0.949 times the radius from the center of the duct.

This procedure would give correct results if the velocity measured a t each location were the true mean velocity for its zone. The correctness of th a t assumption should be examined. W ith turbulent flow, P randtl3 and others have shown tha t the velocity of flow along a smooth boundary is proportional to the seventh root of the distance from the boundary for moderate Reynolds’ numbers and to the eighth root for high Reynolds’ numbers. The author has investigated this law by traverses with a very small impact tube in round and square ducts over a considerable range of air velocities. His observations verify those of Prandtl.

Assuming the seventh-root law to hold, for a duct of radius R, the velocity a t a distance y from the boundary is given by V = k y / \ where k R ^ 7 is the center-line velocity. The mean velocity for the whole duct is 49/60 times the center-line velocity. The mean velocity in any annular area with boundaries yi, y% is given by the expression

872 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERSlocation is a t a distance of 0.961 R from the center instead of the standard 0.949 R. In large ducts, the seventh-root law may not apply to the whole outer ring. In this case the error resulting from the use of the standard pitot-tube location will be increased and the proposed new location, while inaccurate, will still be preferable. The velocity curve for the outer fifth of the area

and the locations of the standard and the correct pitot-tube lo c a t io n s a re shown in Fig. 1.

The standard procedure for a pitot-tube traverse de­fines the minimum number of readings as 10 per diame­ter. A comparison of vol­umes determined by 10- and 20-point traverses (per di­ameter) shows a difference th a t does not exceed 0.4 per cent, which may be re­garded as within the errors of observation. I t would appear th a t a 10-point tra ­verse is sufficient.

Rectangular ducts are permissible according to the A.S.H.&V.E. Standard Test Code. Pitot-tube readings are taken a t the centers of equal areas over the cross- section. The number of these equal areas must not be less than 16 and need not be more than 64. W ith less than 64 readings the

centers must not be more than 6 in. apart. The author has compared volume measurements in a duct which changes from round to rectangular with standard transformation piece and standard duct lengths. The results showed rectangular-duct volumes about 1.3 per cent less than the round-duct volumes but this result should not be generalized, especially as the rectangular duct was smaller than the round duct. In general it would ap­pear to be undesirable to use rectangular ducts for accurate work because of the larger ratio of boundary to cross-section and also because of the lower rigidity of the structure and the consequent changes in form of the duct as the static pressure changes.

Summing up, it would appear tha t the standard procedure with a round duct and 10-point traverses but with changed location of the outermost pitot-tube position would give correct volumes if the pitot tube is accurate, if the flow is axial, and if there is no appreciable pulsation.

P i t o t -Tt jb e E r r o r s

The pitot tube described in the A.S.H.&V.E. Standard Test Code for Fans is indefinite in one respect. Considering, for the purposes of description, tha t the tube is oriented for a vertical traverse, the code drawing shows the tube with three static orifices on one side, each 0.02 in. in diameter. The text states tha t there shall not be fewer than four orifices, not exceeding 0.02 in. in diameter, but does not specify their locations. Presum­ably it is intended to have three orifices on each side of the tube. The practise of many investigators is to have one or two orifices in each side, the top, and the bottom of the tube. So long as the tube is oriented in the direction of the air stream, these various arrangements give identical results.

F i g . 1 V e l o c i t y D i s t r i b u t i o n N e a r B o u n d a r y o p a D u c t

If, however, the directions of the pitot tube and of the air flow do not coincide, the location of the static orifices becomes im­portant. W ith orifices in the sides only, the variation in velocity head which results from a rotation of the tube stem is as shown in Fig. 2. The maximum value is obtained with correct orientation, and this value falls off 2 per cent for a 10-deg and 5 per cent for 20-deg deviation.

If the static orifices are located a t the top and bottom of the tube, the tube has the entirely different characteristic shown in Fig. 3. The velocity-head reading increases with the inclination of the tube to a maximum of about 11 per cent a t a 30-deg incline

Inclination of Tube, De^

F i g . 2 A .S . H .& V .E . P i t o t T u b e

Inclination o f T u b e , Deg

F i g . 3 P i t o t T u b e W i t h S t a t i c O r i f i c e s a t T o p a n d B o t t o m

tion and then comes back to its correct value a t an inclination of about 45 deg. The inclination of the tube in this discussion is assumed to result from the rotation of the stem of the pitot tube.

These results are in accordance with well-known aerodynamic phenomena. W ith the holes in the sides of the tube, inclining the tube to the air stream results in impact effect on the holes presented to the stream and vacuum on the holes on the down­stream side of the tube. As the impact pressure is greater than the vacuum (as shown by numerous test results) the apparent

AIR FLOW IN FAN-DISCHARGE DUCTS PTC-56-2 873

static pressure will be increased and consequently the velocity head (which is the difference between impact and static pressures) will be decreased. W ith the holes a t the top and bottom of the tube, inclining the tube results in a flow of air past the holes which, in the direction of air flow, are now located a t the ends of the short axis of an elliptical tube section. As the inclination in­creases, the long axis of the ellipse shortens until a t a 90-deg in­clination the section becomes circular. Aerodynamic theory shows tha t the velocity of the air a t the locations of the holes will change from v (the velocity of the general air stream) when the tube is correctly oriented, to 2v when the tube is a t 90 deg to the

70 60 50 40 30 20 10 0 10 20 30 40 50 60 70

In c lin a t io n o f T u b e , Deg

F i a . 4 P i t o t T u b e W i t h S t a t i c O r i f i c e s a t S i d e s , T o p , a n d B o t t o m

F i g . 5 P i t o t T u b e W i t h S t a t i c O r i f i c e s a t S i d e s , T o p , a n d B o t t o m b u t W i t h O n e S i d e O b i f i c e P a b t l y P l u g g e d

air stream. As the inclination of the tube increases, the velocity head at the static orifices increases and the static pressure must decrease correspondingly. Consequently, the velocity head indi­cated by the pitot tube will increase.

With static orifices at the sides and also on top and bottom, the pitot-tube characteristic is shown in Fig. 4. I t will be seen that the indicated velocity head increases negligibly and tha t it re­mains practically constant for an inclination of about 25 deg on each side of the correct orientation.

A possible source of error is shown in Fig. 5, which is for a tube with static orifices on the sides as well as top and bottom. The unsymmetrical characteristic curve in this case was found to be due to the fact tha t the inner tube was bent slightly and caused some constriction on one side of the tube. I t shows tha t side orifices are very sensitive to slight clogging.

In Europe two types of pitot tube are used. The Brabble tube is similar to the A.S.H.&V.E. tube but has its static orifices a t the extremes of two diagonal instead of the vertical and hori­zontal diameters. The characteristics of this tube are shown in Fig. 6.

F i g . 6 B r a b b l e T u b e W i t h S t a t i c O r i f i c e s a t t h e E x t r e m i t i e s o f T w o D i a g o n a l s

F i g . 7 P r a n d t l T u b e

The most widely used European form of the pitot tube is the Prandtl tube; the characteristics of this tube are shown in Fig. 7. I t will be seen tha t the velocity-head reading is constant for an inclination of 15 deg on each side of the correct orientation. The static orifices are replaced by a comparatively wide slot so tha t the possibility of clogging is greatly reduced.

A x i a l F l o w

The direction of flow of the air in a fan-discharge duct will

874 TRANSACTIONS OF TH E AM ERICAN SOCIETY OF MECHANICAL ENGINEERS

depend upon the character of the flow as the air enters the duct. Minor eddies are excluded from this discussion. If the air enters with flow parallel to the axis of the duct, it is to be presumed tha t such axial flow will continue. If, however, the air discharges from a propeller fan into the duct, the air will enter with a marked rotational or swirling flow and this will persist for a con­siderable distance. At the usual measuring location of 7.5 diameters along the duct, the whirl will continue with but small abatement. Such rotational flow is to be found not only in the discharge from propeller fans but also from certain centrifugal fans.

The influence of the existence of a tangential component to the

F i g . 8 C o r r e c t i o n F a c t o r sCurve o, Correction factor for tube inclination.Curve b, Correction factor for Prandtl tube. _Curve c, Correction factor for pitot tube with static orifices a t sides, top, and bottom.Curve d, Total correction factor for Prandtl tube.Curve e, Total correction factor for pitot tube with static orifices a t sides, top, and bottom.C u rve /, Total correction factor for A. S.H.&V.E. tube.

air flow on the accuracy of volume determination by a pitot-tube traverse is twofold:

(1) The pitot tube is oriented in an axial direction while the air stream is inclined to th a t direction. The influence of this inclination on the pitot-tube reading has been discussed in the preceding section. If the inclination is known, and also the pitot-tube characteristic, it is possible to obtain a corrected pitot- tube reading.

(2) The corrected pitot-tube reading gives the correct velocity head of the air and from this there can be obtained the velocity along the path of flow. The volume flowing past any element of the cross-sectional area is equal to the axial component of the velocity multiplied by the area of the element. If, at the element considered, the direction of flow is inclined a t an angle a to the axial direction, the axial component is v X cos a.

If the pitot-tube characteristic is known and if the angle of whirl of the air is observed a t each of the pitot-tube stations, it is possible to calculate the volume flowing from a standard pitot- tube traverse. In Fig. 8, the curve a is a cosine curve and gives the correction factor for non-axial flow. Curves b and c are correction factors for pitot-tube errors resulting from inclination of the air stream; they are the reciprocals of the square roots of the values given in Figs. 7 and 4, respectively.

Multiplying correction factor a by the factor b (if a Prandtl tube has been used) gives the total correction factor, curve d. To ob­tain the correct axial velocity a t any point, the velocity calculated in the standard manner must be multiplied by a total correction factor which for the Prandtl tube may be taken from curve d.

If this is done a t each of the standard pitot-tube stations, the actual volume of air flowing can be obtained.

Curve e gives the total correction factor for a pitot tube with static orifices in the sides, top, and bottom. C u rv e/ gives values for the standard tube with static orifices in the sides only.

In order to ascertain whether the air has swirling motion, tra ­verses were made in various discharge ducts with a transverse tube devised by the author.4 This instrument is of great sensi­tivity and will give flow directions with an accuracy better than one degree. In making a traverse along the diameter of the duct it will give the true angle of flow unless there is a radial compo­nent. The investigations of the author do not indicate the pres­ence of any such component.

F i g . 9 A n g l e o f W h i r l o f A i r S t r e a m F r o m a 2 4 - I n . G e n e r a l E l e c t r i c P r o p e l l e r F a n D i s c h a r g i n g I n t o a 2 5 - I n . D o o t

F i g . 1 0 A n g l e o f W h i r l o f A i r S t r e a m F r o m a 3 2 - I n . S i n g l e - I n l e t S t u r t e v a n t F a n D i s c h a r g i n g I n t o a 2 4 - I n . D o c t

4 “The Determination of the Direction and Velocity of Flow of Fluids,” by L. S. Marks, Jour. Franklin Inst., vol. 217, Feb., 1934.

AIR FLOW IN FAN-DISCHARGE DUCTS PTC-56-2 875

With a General Electric Company fan of the propeller type and of 24-in. diameter, discharging into a duct, the observed di­rections of air flow are shown in Fig. 9. The duct was 25 in. in diameter and the fan operated a t 800 rpm. For the outermost 6 in. of the radius the inclination of the air stream was fairly con­stant at a value of about 30 deg. For the inner 6 in. the inclina­tion varied in almost direct proportion to the radius. Careful pitot-tube traverses of the duct by the standard method gave a value of the volume of air flow which was 13.7 per cent higher than that obtained by a pitot-tube traverse in the same air after it had passed through a straightener. Correcting the observed velocity heads by the factors of curve e, Fig. 8, the resulting calcu­lated volume is found to agree with the straightened flow value within 0.3 per cent.

An investigation of the swirl angles was made also in an experi­mental single-inlet, radial-type, 10-blade Sturtevant fan of 32-in. diameter, 19.5-in. inlet diameter, operating a t 1290 rpm. The angles are shown in Fig. 10. This fan gave a pitot-tube-volume measurement which was 6 per cent greater than the simulta­neously observed nozzle volumes. Correcting the pitot-tube- velocity measurements by the use of curve e, Fig. 8, resulted in almost perfect agreement between the pitot-tube and nozzle- volume measurements.

A similar investigation of a single-inlet, backwardly curved

F i g . 11 A n g l e o f W h i k l o f A i r S t r e a m F r o m a 3 4 V 2 - I n . S i n g l e - I n l e t S t d r t e v a n t F a n D i s c h a r g i n g I n t o a 3 2 - I n . D u c t

blade S turtevant fan of 34.5-in. diameter, operating a t 720 rpm gave the air-swirl angles shown in Fig. 11. W ith this fan the pitot-tube traverse gave volume measurements which were 9 per cent greater than the simultaneous nozzle-volume measurements. Corrected for the angle of swirl by the factors given in curve e, Fig. 8, the corrected pitot-tube volumes become only 1.5 per cent greater than the nozzle volumes.

The three fans just discussed are the only fans, showing a dis­crepancy between pitot-tube and nozzle-volume measurements, which have been available to the author for investigation. While it is obviously desirable to extend this investigation to other fans,

F i g . 1 3 A x i a l , T a n g e n t i a l , a n d A n g u l a r V e l o c i t i e s o n a H o r i z o n t a l T r a v e r s e o f t h e D i s c h a r g e D u c t o f a 3 2 - I n . S i n g l e -

I n l e t S t u r t e v a n t F a n

F i g . 12 A x i a l , T a n g e n t i a l , a n d A n g u l a r V e l o c i t i e s o n a H o r i z o n t a l T r a v e r s e o f t h e D i s c h a r g e D u c t o f a 24-In .

G e n e r a l E l e c t r i c C o . P r o p e l l e r F a n

F i g . 1 4 A x i a l , T a n g e n t i a l , a n d A n g u l a r V e l o c i t i e s o n a H o r i z o n t a l T r a v e r s e o f t h e D i s c h a r g e D u c t o f a 3 4 1A - I n .

S i n g l e - I n l e t S t u r t e v a n t F a n

it appears justifiable to conclude, for the present, tha t the m ajor portion of the discrepancy is due to the rotational motion of the air stream.

A n a l y s i s o f t h e W h i r l i n g F l o w

In order to obtain more information as to the character of the whirling flow shown in Figs. 9, 10, and 11, further analyses were made. Applying the correction from curve e, Fig. 8, to the velocity-head readings of pitot-tube traverses, gives the correct axial velocities; from the angles of Figs. 9, 10, and 11 the tan-

876 TRANSACTIONS OF TH E AM ERICAN SOCIETY OF MECHANICAL ENGINEERS

gential velocities are then obtained. These are shown in Figs. 12,13, and 14. From the tangential velocities the angular veloci­ties of whirl were calculated and are also shown.

I t will be observed tha t in Fig. 14 the angular velocity reaches a peak in the center and falls off very rapidly as the radius increases. While the rate of decrease of angular velocity is not as rapid as in a free vortex, there is a definite approximation to tha t type of flow.

W ith a true whirling motion, centrifugal forces will be set up which will cause an increase of static pressure from the center

F i g . 1 5 S t a t i c P r e s s u r e V a r i a t i o n o n a H o r i z o n t a l T r a v e r s e o f t h e D i s c h a r g e D u c t o f a 3 4 > /2 - I n . S i n g l e - I n l e t S t u r t e v a n t

F a n

outward. This was investigated by making a differential static- pressure traverse in the discharge duct of the 34.5-in. Sturtevant fan (Fig. 11), keeping one static tube a t the center, and shifting another static tube to the various standard pitot-tube-traverse stations. The tubes were connected to opposite ends of a man­ometer. The static tubes used were the American Society of Heating and Ventilating Engineers pitot tubes which, as shown later, are not affected by inclination to the air stream. The re­sults of this traverse are shown in Fig. 15. I t is seen tha t for about two-thirds of the radius, the static pressure increases in direct proportion to the radius, and tha t, for the outer third, the static pressure is constant. Approximate calculations of the increase of static pressure with whirling flow agree fairly well with the measured values.

S i n g l e - a n d D o u b l e - I n l e t F a n s

Whirling flow is of occasional occurrence in fan discharge ducts. The investigation of a double-inlet fan which gave almost perfect agreement between pitot-tube and nozzle-volume measurements showed axial flow of the air with no perceptible tangential com­ponent. I t is thought tha t this may be a general condition.

In a single-inlet fan the air enters in a direction transverse to the direction of flow in the discharge duct and, under certain conditions, this component of flow may persist into the discharge duct and may give rise to a whirling flow. W ith a double-inlet flow the two opposed entering air streams will presumably neu­tralize one another in so far as the transverse component is con­cerned. If this is the case, the discrepancy between pitot-tube and nozzle volume measurements (resulting from whirl) should exist only in single-inlet fans. Table 1 of Hagen’s paper2 lists 14 fans, of which five are double-inlet. Four of the double-inlet fans show no volume discrepancies and one only shows a compara­tively small discrepancy. Of the nine single-inlet fans, seven show discrepancies, in most cases of considerable magnitude (from 8 to 18 per cent).

The Hagen data are supported by the more limited tests by the

author which have shown appreciable volume discrepancy only in the case of single-inlet fans. The number of published fan tests in which both methods of volume measurement have been used is too small to permit of final conclusion but the presumption ap­pears to be considerable tha t whirling flow is frequent with single­inlet fans.

There is still further evidence of whirling flow from single-inlet fans in the experience of manufacturers who have developed and tested a single-inlet fan and have later converted it into a double­inlet fan, in effect, by placing two single-inlet fans back to back. With pitot-tube volume measurements the single-inlet fan under these conditions shows larger volumes (per inlet) and conse­quently higher efficiencies than the double-inlet fan. With nozzle volume measurements the reverse is the case. The B. F. S turtevant Company have supplied the author with the perform­ance curves of a fan which was converted from single-inlet to double-inlet in the manner indicated. The pitot-tube volumes for the single-inlet fan under rated conditions are about 4 per cent greater (per inlet) than for the double-inlet fan. The volume measured by a nozzle for the double-inlet fan agrees with the pitot-tube volume but for the single-inlet fan the volume (per inlet) is slightly lower than for the double-inlet fan.

S t r a i g h t e n e r s

If pitot-tube volume measurements are to be made in fan-dis­charge ducts, it is desirable to take any tangential component out of the air flow before such measurements are made. The pro­cedures described above would apparently yield accurate values of the volume but they are better adapted to a research than to a testing laboratory. I t is possible to make the air flow axially by the use of straighteners. For this purpose, a simple egg crate has proved entirely adequate. In the author’s laboratory such egg crates have been made of ‘/ (-in. plywood with cells either2 in. or 3 in. square and 9 in. long. Each partition was rounded (by a sanding machine) on the upstream side and tapered to a fine edge (by a circular saw) on the downstream side, so as to approximate to a streamline section. This procedure is prob­ably of no appreciable value when the straightener is functioning as such, since, in this case, the air approaches a t an angle and eddy formation results. The only value of this refinement is when the egg crate is used in air which is already flowing axially— in this case, it should reduce the pressure drop through the egg crate. An egg crate which is made of sheet metal serves equally well.

I t has been found tha t pitot-tube observations made down­stream from the egg crate should be a t least 3 ft away from it. Closer than this there may be irregularities resulting from minor eddies set up by the partitions.

The use of straighteners of the type described has been found to be completely effective. Even in the case of the General Electric propeller fan described earlier, with a volume of discrepancy of 13.7 per cent, the air flow is completely straightened on flowing through an egg crate with cells 2 in. square and 9 in. long.

In the 34.5-in. single-inlet Sturtevant fan with a discrepancy of 9 per cent, the discrepancy disappears entirely when the pitot- tube traverse is taken on the downstream side of an egg crate with cells 3 in. square and 9 in. long.

On the other hand, in a discharge duct with no volume dis­crepancy, the pitot-tube volume measurements before and after an egg-crate straightener are in close agreement.

I t would appear from the above tha t the simplest way out of the fan-testing difficulties which result from the observed occa­sional volume discrepancies is the use of straighteners. These are very inexpensive and easily and quickly fabricated and are much preferable, in these respects, to the alternatives of nozzles and orifices. The only objection would seem to be in the pressure

AIR FLOW IN FAN-DISCHARGE DUCTS PTC-56-2 877drop which will not permit testing in a wide open condition, but, even here, the pressure drop will be very considerably less than with a nozzle or orifice.

C o n d i t i o n s R e q u i r i n g S t r a i g h t e n e r s

I t is easy to determine whether the air flowing in a duct has rotation, by the use of the transverse tube devised by the author. If such a tube is not available a standard pitot tube located mid­way between the center and the wall of the duct and facing up­stream should be rotated slowly and the maximum velocity-head reading noted. Velocity heads should then be read for inclina­tions of the pitot tube of 30 deg on each side of the position paral­lel to the axis of the duct. If the flow is axial, these two readings will be substantially the same. If there is rotational motion of the air, the readings will differ by an amount which is a function of the inclination of the air flow to the axial direction. With the A.S.H.&V.E. pitot tube, the difference, expressed as a percent­age of the maximum velocity-head reading, is given in the follow­ing table:Angle of swirl, deg.................................................. 5 10 15 20 25Velocity head difference, per cent...................... 15 32 50 72 90These values are readily obtained from Fig. 2.

An examination of Fig. 8 indicates tha t the error resulting from an angle of swirl up to 10 deg is negligible. I t is suggested that, when using the standard pitot tube, the use of a straightener is not necessary unless, in the test just described, the velocity-head difference exceeds 30 per cent of the maximum velocity head.

L e n g t h o f D i s c h a r g e D u c t

The A.S.H.&V.E. Test Code specifies a discharge duct whose length is 10 times its diameter. The author has made volume determinations by pitot-tube traverses at various locations in a discharge duct of that length.

For a double-inlet fan, having no appreciable rotation of the air stream and with a diffuser integral with the fan housing and a transformation piece, each about one diameter in length, the fol­lowing results were obtained; the locations are expressed in diameters from the transformation piece.Location, diam ........................................ 2 .5 5 8 .1 9Volume, cfm at 750 rpm...................... 34450 34580 34530 34330Volume, cfm at 500 rpm ...................... 23200 23250 23200 23000

It is evident that these results are identical—closer than can be obtained except with very accurate work. For such a case a pitot-tube traverse a t 2.5 diam is as satisfactory as one a t 9 diam.

F i g . 16 D i s c h a r g e O r i f i c e s

For a single-inlet fan, having considerable rotation of air stream, without diffuser, but with a transformation piece, similar observations yielded the following results:Location, diam ....................................................... 2 .8 5 .8 8 .8Volume, cfm ............................................................ 10,330 10,275 9940Relative volum es................................................... 1 .04 1.033 1.00

If a straightener is used and located 1 diam from the trans­formation piece, a pitot tube located 3 ft past the straightener will give accurate results. For a 3-ft duct, this will fix the pitot-tube

location a t 2.5 diam from the transformation piece. The author’s tests made on the single-inlet fan just discussed show perfect agreement between volume measurements behind a straightener located (1) a t one diameter from the transformation piece and (2) a t eight diameters from the transformation piece.

If the capacity of the fan is varied by attaching orifices at the duct exit, the question arises as to what length of duct is necessary past the pitot-tube location. The author has investigated this question in the following manner. W ith a double-inlet fan, having no rotation of air, the volume of air flowing was kept con­stant, by varying the rpm, under three conditions of operation: (1) with wide open discharge, (2) with discharge through a smaller circular orifice, and (3) with discharge through an annular opening. These conditions are shown in Fig. 16. Pitot-tube traverses were taken 2.5 diam upstream from these orifices. The velocity-head distribution was found to be identical for all three cases. I t is concluded tha t, with 2.5 diam of duct past the pitot-tube station, there is no disturbance of the pitot-tube readings resulting from the presence of obstructions a t the end of the discharge duct.

I t is tentatively suggested tha t the total length of the discharge duct may be reduced to 5 diam when the whirl is taken out of the air.

Shortening the duct will have the beneficial effect of reducing or eliminating the friction correction which is specified in the A.S.H.&V.E. Fan Test Code. The specified correction appears to be too great and should be reconsidered in any case. If, however, a straightener is used and the static pressure is measured at not more than 1 diam down the duct, the duct friction in that length will be so small as to be entirely negligible.

S t a t i c -Pr e s s u r e M e a s u r e m e n t

The readings of static pressure by a p ito t tube are affected by inclination of the tube to the air stream. The magnitude of this effect can be seen in Figs. 2, 3 ,4 ,6 , and 7. In these figures, static- pressure change is shown in terms of velocity head. For ex­ample, if the static pressure is shown as 0.9, the indicated static pressure will be less than the actual static pressure by one-tenth of the velocity head.

For convenience, this information is summarized in Table 1, which gives the error in the static-pressure reading as a percentage of the velocity head. A minus sign indicates tha t the reading is low.TABLE 1 ERROR IN STATIC PRESSURE AS PERC EN TA G E OF VELOCITY HEADInclination of tube, deg............................................ 10 20 30A.S.H.&V.E. tu b e ...................................................... 1 1 1Tube with holes a t sides, top, and bo ttom ............. ...—3 — 8 — 16Tube with holes at top and bottom:Brabble tu b e ..............................................................—3 — 10 —20Prandtl tube ...............................................................— 1.5 — 8 .5 — 16

I t will be seen tha t the A.S.H.&V.E. tube gives remarkably constant values of static pressure and tha t its error is not likely to be greater than one per cent of the velocity head. The readings are quite sensitive to workmanship in making the pitot tube. The static orifices must be of the same number on both sides of the tube and must be very accurately of the same diameter.

The actual static-pressure reading is equal to the true static pressure plus or minus a fraction of the velocity head. At wide- open operation, where static pressure is low and velocity head is high, the error of the static reading due to tube inclination may be a large fraction of the true static pressure, but the static efficiency for this condition is usually of little importance. Under normal operating conditions for most fans, the static pressure is greater than velocity head and the error becomes of less importance. For example, with a fan operating a t a 2-in. static pressure and a 1-in. velocity head, a rotation of the air stream which results in

878 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERSincreasing the static reading by 2 per cent of this velocity head, would change the static reading from 2 to 2.02 in. or by one per cent.

I t is therefore suggested tha t in a rotating air stream the static pressure can be obtained with sufficient accuracy for fan-testing purposes, by the use of the A.S.H.&V.E. pitot tube.

A.S.H.&V.E. T u b e a n d P r a n d t l T u b eA comparison of Figs. 2 and 7 indicates the relative advantages

of these two tubes. The Prandtl tube has a flatter characteristic for velocity head and consequently will give more nearly accurate volumes with rotating flow. If straighteners are used, there is no choice between them in this respect.

In regard to static-pressure measurements, the A.S.H.&V.E. tube is much superior to the Prandtl tube. This superiority de­pends on the condition of the tube. If any of the holes become clogged, the tube characteristic changes radically. The Prandtl tube is comparatively free from liability to clogging of the static slot.

V e l o c it y H e a d a n d T o t a l P r e s s u r eWhere rotating flow exists, there arises the need of a definition

of velocity head for use in computing the total pressure and total efficiency of a fan. The velocity head may mean either (1) the actual velocity head along the actual path of flow (average for the whole cross-section) or (2) the velocity head corresponding to the mean axial velocity. This is a m atter for arbitrary decision.

From a practical standpoint it would seem tha t the mean axial velocity should be chosen.

The total pressure then becomes the sum of the static pressure (measured before the straightener) and the velocity head ob­tained from measurements past the straightener. No correction for duct friction is necessary.

C o n c l u s io nThe preceding discussion leads to the following suggestions in

the testing of fans discharging into ducts:(1) Modification of the standard pitot-tube locations.(2) A preliminary investigation of the character of the air flow

in the duct by means of a transverse tube or a pitot tube, and the use of an egg-crate straightener in case the air is found to be ro­tating more than a stated amount, or preferably.

(3) The prescribed use of a straightener in all cases.(4) A more precise specification for the standard pitot tube.(5) The shortening of the discharge duct and the possible elimi­

nation of the duct friction correction.(6) A new definition of velocity head.

A c k n o w l e d g m e n t sAcknowledgment is made, for assistance in conducting the

numerous investigations on which this paper is based, to a number of graduate students in the Harvard Engineering School and, in particular, to Randolph Ashton, Thomas Flint, and R. Beeuwkes.