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Contribution to round table discussion on plume rise and dispersion
Atmospheric Environment, Pergamon Press 1968. Vol. 2, pp. 247-250. Printed in Great Britain.
CONTRIBUTION TO ROUND TABLE DISCUSSION PLUME RISE AND DISPERSION
ON
of Dr. BRUMMAGE’S paper in the Journal marks something of a departure from normal practice in that it does not contribute anything new in the way of experimental data or understanding of the physical nature of the problem discussed. However, it is of value in that it serves to illustrate the dilemma of organizations concerned with giving advice on the construction of plant when confronted with the multiplicity of plume rise formulae, a different one it seems from each group of investigators. The result, in this particular case, has been to produce yet another plume rise formula, which has already found its way into the literature (SIIXN, 1968) where it has made the top seven. The dif8culties arise largely from the fact that while there is now a considerable volume of data on the rise of plumes from large plant with heat emission of 20 MW (i.e. 5 Meals set-I) and above from CEGB (HAMILTON, 1967) and TVA at distances of around 1 mile downwind from the source, there is a very serious lack of data for the medium-sized plant with which the CONCAWE organization is primarily concerned. (Heat emission range l-10 MW.) The RUJCH (1964) data, which dominate the CONCAWE analysis, consist of measurements which reached 500 m downwind on only 10 per cent of the occasions when the plumes were photographed. For this reason it would be rather unwise at this stage to support or condemn the CONCAWE procedure or to suggest an alternative for plant in this size range until these data are to hand. There are also some points of accuracy which require comment. THE PUBLICATION
Section 3.3
The statement to the effect that the LUCAS,M~~REand Spurta (1963) equation gives rises which are high compared with practice, if by practice one meuns observation, is probably correct in the context of the paragraph in which it occurs (i.e. volume emissions of 20-50 Nm3 set-I). HAMfLTON (1967) has remarked that the plume rises observed by BAUCH(1964) were lower than the equation indicated, even when allowance was made for the short distance from the stack at which they were measured. The next paragraph however is misleading. 100 Nm3 set-1 does not extend beyond the great bulk of the observations (even then available) if the Earley and Castle Donington observations are given proper weight. The L&s et 01. equation fits these observations whereas the CONCAWE equation gives rather lower values. The paragraph under discussion ought to state that the CGNCAWE equation is no longer applicable at this rate of heat emission (30 MW at 250°C temperature excess). This inference is con6rmed by the comparison with the TVA data in Table 9. Most of these were measured at 800 m downwind and were not the 6nal rises of the plume. Even so, the heights attained were somewhat underestimated by the CONCAWE equation. Section 4.1
Briggs in his contribution to this discussion has pointed out that the power law relationships batween the various parameters depend upon the form of the assumed plume rise equation. Pasquill in his contribution points out that the Wipperman and Klug relationship.
where R = (m,+mJm, (this appears on p. 20 of the original CGNCAWB booklet) also a&&s this power law dependence. We can write down a general expression equivalent to the speci6c expressions given in Briggs’s Table 1, viz Ah
_
MPQ/
uB
, L= K,D"Qp,
l-A/B 1 I1=(R+p-l/B) andzz=(R+p-l/B). 247
248
D. J. MYIODRE
The values of (O&J,.) implicit in the factor D would now refer to a fixed distance (say 1000 m). The turbulence measurements reported by MOORE(1967) indicated that m, = 0.6 and m, = O-9 for a 1 hr sampling time in strong wind turbulent conditions, i.e. that R = 2~5. ff this value of R and value ofp = 9, A = 2, and B = 1, appropriate to the CERL formula are used then II = 0545 and I, = 0.409. These are very close to the values suggested by ASME @ = 0, A = 1, B = 3, R = 2) and Brig$s (R=),A=&B=l,R=2)ofi,=0~6andIa=@4. Mr. G. Spurr has provided an equation refating stack height to total heat up the stack for CEGB power stations ranging in size from 130 MW to 2000 MW of ge~e~atj~g capaeily* per stack. This equation is Jr = 66 Qho’385 (& in MW)
(I.e. f, -0-4).
(Strictly one wants a ~lationship with sensible heat, but this is not 1ikeIy to be very different in form.) Therefore, for large plant with heat emission above 20 MW and stack height of 90 m or more, current practice and formulae indicate that stack height should increase roughiy as the 8 power of the capacity of the pfant. There is no serious disagreement here with the CGNCAWE approach, which indicates that stack height should increase as the square root of plant capacity. The big difference is in the value of II which the CONCAWE (p = 0, A = 4, B = 2, R = 2) equation indicates is 1.5. This point illustrates the importance of realizing that the forms of the nomograms Figs. 5,8 and 9 depend very critically on the values of the indices used in the diffusion and plume rise equations. Other contributions in this and preceding issues of the Journal e.g. SCHMIDT(1965), LUCAS(1967), SCORER (1968) provide alternative approaches and the reader is invited to peruse these and draw his own conclusions as to the procedure which would be most suitable in his particuiar case.
Some gene& remarks on pIume rise fn an earlier paper I discussed some of the implications of the physical nature of piumes (MOORE, differed depending on whether they {a} remained continuous in the downwind direction (C-plumes) or (b) broke up into fumps which then remained separate @-Plumes) during the period which determines the rise or (c} grew together again (R-Plumes) during this period. The apparent anomalies in the observations (e.g. the low values of rise observed by RAUCH (1964) ) can be explained quite satisfactorily by assuming that plumes from small sources (less than 10 MW) are L-Plumes and plumes from larger plants are R-Plumes (or if it is prefered, C-Plumes). TABLE 1 illustrates the main features of four of the simpler models. In this table numerical values have been assigned to the arbitrary constants introduced in the models. It is also worth noting that the R-Plume and the LUCAS, M~J~REand SPURR (1963) modification of Prieststfey’s model are identical in form except for the interpretation of the nature of the spreading coefficient (C), Also the ratio of the rises predicted by the R-Plume and C-Plume models is 1966). Eehaviour
i.e. they agree with 10 per cent over the range l-8 c(x/&) c 22 which covers most of the measurements made at large power plants. The Lucas, Moore and Spurr equation is “dimensionally correct” if a term which would be almost constant at a dven plant and vary roughly as Q l/l6 from plant to plant is introduced. The spreading coefficient C has been shown by VADOT(1965) to be a function of variables [essentially the dimensionless quantities (u/w,) and(gQ/npC,,Q,dw,“)] which can be combined to give the required slowly varying term (see column 3 of TABLE1). The real differences in the application of the equations lie in the termination of the rise to gain a ptume height to substitute in the diffusion equation. My own view here is that if the plume has become sufficiently dilute for its lower edge to be in contact with the ground, al] effective buoyancy must have been lost at half or less of the distance from the stack where the maximum surface concen+ Sensible heat emission z & generating capacity.
n/
..\
where
Continuous plumes C-plume Ref. SCORER(I 958)
Volume of lump = +?Z3
U= wind speed
Material emitted in arbitrary time T remains withinvolume element nczzzur i.e. horizontal continuity.
(Lumps combine as plume drifts downwind). L-plume Heat content does not change. (Lumps do not recombine) Ref. RICHARDS(1965); M~~RE (1966)
a = const. (about 4).
E(L,+z),
L, = 3d (d = stack dia.)
of heat
Plume splits into puffs initially containing
Lumpy plume model. R-plume Heat content of lump increases with distance (x) m as
‘&units cl
C* = const U (actually Priestley assumed a Gaussian distribution of material within the plume)
Material emitted in arbitrary time T remains within volume element nCrZrW7 i.e. vertical continuity.
Vertical plume. Ref. PR~E.YTLEV and BALL (1954); PRIE~TLEY(1956)
C’ = const.
-
(g&yg)
Theoretical expressions’ for plume height during buoyancy dominated stage (i.e. when atmospheric turbulence is not important in spreading the plume)
Qincabwc-’ P am-’ C, cab des- ’ a- ’ 0. dea K
.
(In LUCAS, MOORE and SPURR, 1963, U/C* was assumed to vary from plant to plant, but remain constant at a given plant)
(i.e. similar form to Priestley)
the usual meaning and dimensions.
Symbols have
simplest expression for this term would therefore be C* or Cs
N.B. Both the above expressions are unsatisfactory in that the constant has dimensions of a velocity. This velocity must be determined by the initial elllux conditions and at the same time must not affect the dependence of the rise on the heat emission a? a given planr: The
cs = const u
Nature of dimensionless spreading coefficient C = (dr/dr) r = plume radius (m)
Geometrical implication z = height above source w = dz/dt
Model
Q,
MW
U
QM*~* tCTj
gmsec-a e, (I dimensionless W, m sa-’ Q,, in MW d0/dz in ‘K m-’
3.3
u
2.7 QMt x’(36d)* (LT)
~dx* cRTj u
Qx> 10 MW
2.7
Numerical values (Qu in MW. d,x, metres U msec- r) (to be used for 2OO
Csanady
Briggs
Ah cc+
Scorer, ASME, etc.
U
U
Ah=330
h
0 loo
33OQ,’
Ah > -
. ..
. ,
+
The final rise of the plume used for calculation of maximum surface concentration, obtained by equating x in previous column to a fixed length xr
1
1
assumed
expression to
X+x
QM US
Plume is considered to have finished rising when plume vertical velocity = atmospheric turbulent velocities
Plume continues to rise according to 3 law until point of max. surface concentration is reached I.e. xr = x,,,
i.e. xr 2 10 h
Plume levels out at x> IO h.
x,0c9(~)?lwo(~)
Lucas (1967) equivalent
Empirical
Plume levels off at a distance determined by height of source and intensity of atmospheric turbulence (i).
for xr
Expression
~ntribution
to Round Table Discussion
on Plume Rise and Dispersion
249
t&on is observed. I find it very difficult to believe that a plume whose average axial height continues to rise can also be in contact with the ground and remain continuous in the downwind direction. The types of plume represented by these equations have all been observed to occur in practice. The dominance of a particular plume type in a particular set of observations will be influenced in part by climatic or seasonal conditions and partly by observational technique, e.g. plume photographs will tend to record the continuous plumes to long distances but lose the plumes which are more affected by atmospheric turbulence (and so produce the highest surface concentrations) nearer the source. In TABLE 2 plume rise values (expressed as C/Z/QDl*) calculated from the lumpy plume equations (recombining for sources greater than 10 MW) are shown to be. in good agreement with rises at various TABLE 2. COMPARISON OF OBSERVED AND
PREDICTED PLUME RESFS(EXPKESED AS (UZ/Qn,f
m2sec-rMW-•))
Intermediate
rises (measured at 500 m or less from the source)
Stack ht. (m) Stack dia. (m) Dist. from source (m) No. of observations Mean value of observed U~lQb2 > calculated Prediction equation (from TABLB 1) Final rises
Stack ht. Stack dia. No. of observations Mean value of observed UZlQHf > calculated
128 3-s 200 500 397 37 123 202 128 204 LT LT (Rauch)
158, 185 7.6, 7.9 450 685 268 258
100 7 400 70 240 238 RT (Tilbury)
(i.e. measured at or beyond 1100 m) 120 6 339 500 522 (Northfleet)
128 7 310 580 540 (Castle D)
70 5 226 460 425 (Earley)
As above As above 1004 556 594 (TVA)
distances downwind from the source. The C-plume equation would also have been in good agreement with the large source rises. There will be di~culti~ in using the lumpy plume models in the region of the transition to the combining plume (- 10 MW heat emission). The best solution would probably be an empirical equation in which the diameter term is phased out between say 5 and 20 MW. As stack height varies roughly as (heat emission)* (see above) and stack height and stack diameter are roughly proportional, it follows that aplant to planf empirical equation in which Q and U are the only variables would be of the form:
i.e. similar to the CONCAWE and CAIGON and MOSES(1967) expressions. The agreement between theory and observaion in TABLE 2 is very close, the mean plume rise being predicted to an accuracy of better than 8 per cent in all cases. Such good agreement is only to be expected where sufficient observations have been made to eliminate the effects of displacement of the phrmes by vertical atmospheric motions.
250
D. J. MOORE
These comparisons consist of actual observations at the distances involved but not extrapolated values. The final rises were all predicted from the RF. equation TABLE1. Stable conditions, i.e.
(g/i3 a@&)> W13W
set-2,
were excluded from the TVA data. CERL
D. J. MOORE
Cfeeve Road, Leatherhead.
Additi~na~ references (i.e. not given by Briggs or Brummuge above) J. E. and MOSESH. (1967) Calculation of effective stack height. Am. Met. Sot. 47th Annual Meeting. Mooas D. J. (1966) Physical aspects of plume models. Air War. Polk Znt. J. 10,411-417. Mooax D. J. (1967) Meteorological measurements on a 187 m tower. Atmospheric Environment 1, 367-377. RICHARIX J. M. (1965) Puff motions in unstratified surroundings. J. Fluid Mech. 21, 97406. SCORERR. S. (1968) Air pollution problems at a proposed Merseyside chemical fertilizer plant: a case study. Atmospheric Environment 2, 35-48. STERNA. C. (1968) Air Polfution. Academic Press, New York. VADW L. (1965) Etude de la diffusion des panaches de fumee duns l’atmosphere. CITEPA Paris. CARSON
CONTRIBUTION TO ROUND TABLE DISCUSSION PLUME RISE AND DISPERSION
ON
of Dr. BRUMMAGE’S paper in the Journal marks something of a departure from normal practice in that it does not contribute anything new in the way of experimental data or understanding of the physical nature of the problem discussed. However, it is of value in that it serves to illustrate the dilemma of organizations concerned with giving advice on the construction of plant when confronted with the multiplicity of plume rise formulae, a different one it seems from each group of investigators. The result, in this particular case, has been to produce yet another plume rise formula, which has already found its way into the literature (SIIXN, 1968) where it has made the top seven. The dif8culties arise largely from the fact that while there is now a considerable volume of data on the rise of plumes from large plant with heat emission of 20 MW (i.e. 5 Meals set-I) and above from CEGB (HAMILTON, 1967) and TVA at distances of around 1 mile downwind from the source, there is a very serious lack of data for the medium-sized plant with which the CONCAWE organization is primarily concerned. (Heat emission range l-10 MW.) The RUJCH (1964) data, which dominate the CONCAWE analysis, consist of measurements which reached 500 m downwind on only 10 per cent of the occasions when the plumes were photographed. For this reason it would be rather unwise at this stage to support or condemn the CONCAWE procedure or to suggest an alternative for plant in this size range until these data are to hand. There are also some points of accuracy which require comment. THE PUBLICATION
Section 3.3
The statement to the effect that the LUCAS,M~~REand Spurta (1963) equation gives rises which are high compared with practice, if by practice one meuns observation, is probably correct in the context of the paragraph in which it occurs (i.e. volume emissions of 20-50 Nm3 set-I). HAMfLTON (1967) has remarked that the plume rises observed by BAUCH(1964) were lower than the equation indicated, even when allowance was made for the short distance from the stack at which they were measured. The next paragraph however is misleading. 100 Nm3 set-1 does not extend beyond the great bulk of the observations (even then available) if the Earley and Castle Donington observations are given proper weight. The L&s et 01. equation fits these observations whereas the CONCAWE equation gives rather lower values. The paragraph under discussion ought to state that the CGNCAWE equation is no longer applicable at this rate of heat emission (30 MW at 250°C temperature excess). This inference is con6rmed by the comparison with the TVA data in Table 9. Most of these were measured at 800 m downwind and were not the 6nal rises of the plume. Even so, the heights attained were somewhat underestimated by the CONCAWE equation. Section 4.1
Briggs in his contribution to this discussion has pointed out that the power law relationships batween the various parameters depend upon the form of the assumed plume rise equation. Pasquill in his contribution points out that the Wipperman and Klug relationship.
where R = (m,+mJm, (this appears on p. 20 of the original CGNCAWB booklet) also a&&s this power law dependence. We can write down a general expression equivalent to the speci6c expressions given in Briggs’s Table 1, viz Ah
_
MPQ/
uB
, L= K,D"Qp,
l-A/B 1 I1=(R+p-l/B) andzz=(R+p-l/B). 247
248
D. J. MYIODRE
The values of (O&J,.) implicit in the factor D would now refer to a fixed distance (say 1000 m). The turbulence measurements reported by MOORE(1967) indicated that m, = 0.6 and m, = O-9 for a 1 hr sampling time in strong wind turbulent conditions, i.e. that R = 2~5. ff this value of R and value ofp = 9, A = 2, and B = 1, appropriate to the CERL formula are used then II = 0545 and I, = 0.409. These are very close to the values suggested by ASME @ = 0, A = 1, B = 3, R = 2) and Brig$s (R=),A=&B=l,R=2)ofi,=0~6andIa=@4. Mr. G. Spurr has provided an equation refating stack height to total heat up the stack for CEGB power stations ranging in size from 130 MW to 2000 MW of ge~e~atj~g capaeily* per stack. This equation is Jr = 66 Qho’385 (& in MW)
(I.e. f, -0-4).
(Strictly one wants a ~lationship with sensible heat, but this is not 1ikeIy to be very different in form.) Therefore, for large plant with heat emission above 20 MW and stack height of 90 m or more, current practice and formulae indicate that stack height should increase roughiy as the 8 power of the capacity of the pfant. There is no serious disagreement here with the CGNCAWE approach, which indicates that stack height should increase as the square root of plant capacity. The big difference is in the value of II which the CONCAWE (p = 0, A = 4, B = 2, R = 2) equation indicates is 1.5. This point illustrates the importance of realizing that the forms of the nomograms Figs. 5,8 and 9 depend very critically on the values of the indices used in the diffusion and plume rise equations. Other contributions in this and preceding issues of the Journal e.g. SCHMIDT(1965), LUCAS(1967), SCORER (1968) provide alternative approaches and the reader is invited to peruse these and draw his own conclusions as to the procedure which would be most suitable in his particuiar case.
Some gene& remarks on pIume rise fn an earlier paper I discussed some of the implications of the physical nature of piumes (MOORE, differed depending on whether they {a} remained continuous in the downwind direction (C-plumes) or (b) broke up into fumps which then remained separate @-Plumes) during the period which determines the rise or (c} grew together again (R-Plumes) during this period. The apparent anomalies in the observations (e.g. the low values of rise observed by RAUCH (1964) ) can be explained quite satisfactorily by assuming that plumes from small sources (less than 10 MW) are L-Plumes and plumes from larger plants are R-Plumes (or if it is prefered, C-Plumes). TABLE 1 illustrates the main features of four of the simpler models. In this table numerical values have been assigned to the arbitrary constants introduced in the models. It is also worth noting that the R-Plume and the LUCAS, M~J~REand SPURR (1963) modification of Prieststfey’s model are identical in form except for the interpretation of the nature of the spreading coefficient (C), Also the ratio of the rises predicted by the R-Plume and C-Plume models is 1966). Eehaviour
i.e. they agree with 10 per cent over the range l-8 c(x/&) c 22 which covers most of the measurements made at large power plants. The Lucas, Moore and Spurr equation is “dimensionally correct” if a term which would be almost constant at a dven plant and vary roughly as Q l/l6 from plant to plant is introduced. The spreading coefficient C has been shown by VADOT(1965) to be a function of variables [essentially the dimensionless quantities (u/w,) and(gQ/npC,,Q,dw,“)] which can be combined to give the required slowly varying term (see column 3 of TABLE1). The real differences in the application of the equations lie in the termination of the rise to gain a ptume height to substitute in the diffusion equation. My own view here is that if the plume has become sufficiently dilute for its lower edge to be in contact with the ground, al] effective buoyancy must have been lost at half or less of the distance from the stack where the maximum surface concen+ Sensible heat emission z & generating capacity.
n/
..\
where
Continuous plumes C-plume Ref. SCORER(I 958)
Volume of lump = +?Z3
U= wind speed
Material emitted in arbitrary time T remains withinvolume element nczzzur i.e. horizontal continuity.
(Lumps combine as plume drifts downwind). L-plume Heat content does not change. (Lumps do not recombine) Ref. RICHARDS(1965); M~~RE (1966)
a = const. (about 4).
E(L,+z),
L, = 3d (d = stack dia.)
of heat
Plume splits into puffs initially containing
Lumpy plume model. R-plume Heat content of lump increases with distance (x) m as
‘&units cl
C* = const U (actually Priestley assumed a Gaussian distribution of material within the plume)
Material emitted in arbitrary time T remains within volume element nCrZrW7 i.e. vertical continuity.
Vertical plume. Ref. PR~E.YTLEV and BALL (1954); PRIE~TLEY(1956)
C’ = const.
-
(g&yg)
Theoretical expressions’ for plume height during buoyancy dominated stage (i.e. when atmospheric turbulence is not important in spreading the plume)
Qincabwc-’ P am-’ C, cab des- ’ a- ’ 0. dea K
.
(In LUCAS, MOORE and SPURR, 1963, U/C* was assumed to vary from plant to plant, but remain constant at a given plant)
(i.e. similar form to Priestley)
the usual meaning and dimensions.
Symbols have
simplest expression for this term would therefore be C* or Cs
N.B. Both the above expressions are unsatisfactory in that the constant has dimensions of a velocity. This velocity must be determined by the initial elllux conditions and at the same time must not affect the dependence of the rise on the heat emission a? a given planr: The
cs = const u
Nature of dimensionless spreading coefficient C = (dr/dr) r = plume radius (m)
Geometrical implication z = height above source w = dz/dt
Model
Q,
MW
U
QM*~* tCTj
gmsec-a e, (I dimensionless W, m sa-’ Q,, in MW d0/dz in ‘K m-’
3.3
u
2.7 QMt x’(36d)* (LT)
~dx* cRTj u
Qx> 10 MW
2.7
Numerical values (Qu in MW. d,x, metres U msec- r) (to be used for 2OO
Csanady
Briggs
Ah cc+
Scorer, ASME, etc.
U
U
Ah=330
h
0 loo
33OQ,’
Ah > -
. ..
. ,
+
The final rise of the plume used for calculation of maximum surface concentration, obtained by equating x in previous column to a fixed length xr
1
1
assumed
expression to
X+x
QM US
Plume is considered to have finished rising when plume vertical velocity = atmospheric turbulent velocities
Plume continues to rise according to 3 law until point of max. surface concentration is reached I.e. xr = x,,,
i.e. xr 2 10 h
Plume levels out at x> IO h.
x,0c9(~)?lwo(~)
Lucas (1967) equivalent
Empirical
Plume levels off at a distance determined by height of source and intensity of atmospheric turbulence (i).
for xr
Expression
~ntribution
to Round Table Discussion
on Plume Rise and Dispersion
249
t&on is observed. I find it very difficult to believe that a plume whose average axial height continues to rise can also be in contact with the ground and remain continuous in the downwind direction. The types of plume represented by these equations have all been observed to occur in practice. The dominance of a particular plume type in a particular set of observations will be influenced in part by climatic or seasonal conditions and partly by observational technique, e.g. plume photographs will tend to record the continuous plumes to long distances but lose the plumes which are more affected by atmospheric turbulence (and so produce the highest surface concentrations) nearer the source. In TABLE 2 plume rise values (expressed as C/Z/QDl*) calculated from the lumpy plume equations (recombining for sources greater than 10 MW) are shown to be. in good agreement with rises at various TABLE 2. COMPARISON OF OBSERVED AND
PREDICTED PLUME RESFS(EXPKESED AS (UZ/Qn,f
m2sec-rMW-•))
Intermediate
rises (measured at 500 m or less from the source)
Stack ht. (m) Stack dia. (m) Dist. from source (m) No. of observations Mean value of observed U~lQb2 > calculated Prediction equation (from TABLB 1) Final rises
Stack ht. Stack dia. No. of observations Mean value of observed UZlQHf > calculated
128 3-s 200 500 397 37 123 202 128 204 LT LT (Rauch)
158, 185 7.6, 7.9 450 685 268 258
100 7 400 70 240 238 RT (Tilbury)
(i.e. measured at or beyond 1100 m) 120 6 339 500 522 (Northfleet)
128 7 310 580 540 (Castle D)
70 5 226 460 425 (Earley)
As above As above 1004 556 594 (TVA)
distances downwind from the source. The C-plume equation would also have been in good agreement with the large source rises. There will be di~culti~ in using the lumpy plume models in the region of the transition to the combining plume (- 10 MW heat emission). The best solution would probably be an empirical equation in which the diameter term is phased out between say 5 and 20 MW. As stack height varies roughly as (heat emission)* (see above) and stack height and stack diameter are roughly proportional, it follows that aplant to planf empirical equation in which Q and U are the only variables would be of the form:
i.e. similar to the CONCAWE and CAIGON and MOSES(1967) expressions. The agreement between theory and observaion in TABLE 2 is very close, the mean plume rise being predicted to an accuracy of better than 8 per cent in all cases. Such good agreement is only to be expected where sufficient observations have been made to eliminate the effects of displacement of the phrmes by vertical atmospheric motions.
250
D. J. MOORE
These comparisons consist of actual observations at the distances involved but not extrapolated values. The final rises were all predicted from the RF. equation TABLE1. Stable conditions, i.e.
(g/i3 a@&)> W13W
set-2,
were excluded from the TVA data. CERL
D. J. MOORE
Cfeeve Road, Leatherhead.
Additi~na~ references (i.e. not given by Briggs or Brummuge above) J. E. and MOSESH. (1967) Calculation of effective stack height. Am. Met. Sot. 47th Annual Meeting. Mooas D. J. (1966) Physical aspects of plume models. Air War. Polk Znt. J. 10,411-417. Mooax D. J. (1967) Meteorological measurements on a 187 m tower. Atmospheric Environment 1, 367-377. RICHARIX J. M. (1965) Puff motions in unstratified surroundings. J. Fluid Mech. 21, 97406. SCORERR. S. (1968) Air pollution problems at a proposed Merseyside chemical fertilizer plant: a case study. Atmospheric Environment 2, 35-48. STERNA. C. (1968) Air Polfution. Academic Press, New York. VADW L. (1965) Etude de la diffusion des panaches de fumee duns l’atmosphere. CITEPA Paris. CARSON