CORRESPONDENCE Lifting and Blowoff of Flames from Short Cylindrical Burner Ports SIR: Reference is made to Channing W. %%on’s paper, “Lifting and Blowoff of Flames from Short Cylindrical Burner Ports,” IND. ENG.CHEM.,44, 2937 (1952)l. Although the experimental data apparently correlatevery well, there are several inconsistencies in the theoretical treatment. Equation 1 is valid for either laminar or turbulent flow, but the resistance or frictional coefficient, X, in Equation 1 is twice the value of X used in Equation 2. Since Equation 2 is used in the development of the final correlation, Equation 2 should be written
Another minor point: I n tho title of Figure 3 the word “parts” should read “ports.” PHILIPE. BocQuwr DEPARTMENT OF PHYSIOLOGY UBIVERSITY OF MICHIGAX A N N ARBOR, MICH.
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SIR: I appreciate X r . Bocquet’s calling attention to an unaccountable omission of a 2 in Equation 2. Equation 4 will then be, accordingly
in order t o be consistent with the X defined in the equatiuns for Cases A, B, and C on page 2941. Equation 1 is applicable only to “established” flow since it is derived on the basis that the velocity near the wall is directly proportional to the pressure gradient along the tube. This condition is not satisfied along the entrance length of any tube. Presumably, the ve!ocity distribution and pressure losses have not been quantitatively determined for a square-edged entrance. Consequently, the distance from a square-edged entrance for a flow t o become established cannot he predicted. Qualitatively, it is known t h a t the pressure losses for a square-edged entrance are much greater than the losses for a rounded entrance and that the velocity distribution is more nonuniform for the squareedged entrance. In other words, the distance from the entrance for flow to become established is a t least as great for a squareedged entrance as for a rounded entrance. Bassinesq [Compt. rend., 113, 9, 49 (189l)l has computed the entrance distance for a rounded entrance to be
X = 0.065 D Re where D is the tube diameter and Re is the Reynolds number. This expression can still be found in modern treatments (Perry, J. H.. ed., “Chemical Engineer’s Handbook,” 3rd ed., p. 388, New York. McGraw-Hill Book Co., 1950). The application of the equation t o Wilson’s most favorable experimental condition-i.?, for Re = 400 and l / r = 10shows t h a t the burner ports are only one fifth of the necessary length for flow to become established. For all other experimental conditions, this fraction of the necessary length is even smaller. In summary. it appears that the right side of Kilson’s Equation 2 should be divided by 2 so that X would have consistent definition throughout the paper. Furthermore, the experimental evaluation of X by Equation 4 even when multiplied by 2, cannot be substituted into Equation 1 since the flow a t the exit of the burner ports is not established for any of the experimental conditions.
It was made clear in an earlier paper [Wilson, C. W. and Hawkins, K.J., IND.ENG.CHEM.,43, 2129 (1951)] and indicated briefly in the present retercnce, that the full streamline or turbulent velocity profile, respectively, is not developed in these short burner ports, whether they have a rounded or a squareedge entrance. They are similar to the entrance section of a tubc in which there is a transition from a uniform velocity t o the established flow profile. The length of the ports n’as in all cases much shorter than the transition length. A theoretical treatment by Schiller [Gebiete Inqenieurw., 248, 5-36 (1922)l permitted him to estimate theoretically the pressure drop coefficient, 1,in the entrance region of a tube having a rounded entrance. This treatment considered the momentum change accompanying the change in velocity profile, the pressui e loss, and the frictional forces. H e found agreement between experimental measurements of pressure loss and his theory, and found t h a t for a given length of the entrance section the value of the coefficient, A, is a function of the Reynolds number. In the absence of a similar theoretical treatment, which would be very difficult for a square-edged entrance, it was not considered unreasonable to attempt the application of values of X derived from the experimentally determined pressure 1 0 ~ 8 , corrected for the kinetic energy change, to the velocity profile Equation 1. The correlation of the blowoff data by means of this procedure seems satisfactory, within the range of variation of the experimental conditions encompassed. However, it should not be concluded that these results can be used to establish the validity of any hypothesis regarding the character of flow in channels of this form. Although there is uncertainty concerning the length and effect of the vena contracta, the limited number of pressure loss measurements which mere made suggest a relationship between X and Re similar to that deduced by Schiller for rounded entrances. I t is regretted that these points were not made more clear in the paper DEPARTMEUT GABELECTRIC LIGHTA X D OF BALTIMORE B A L T I M O R B 3, R f D . REsrARCH
COXSOLIDATED
POWER Co.
1822
CHANNINC
I\‘. WILSON
