To the Editor: I t is unfortunate that the paper by Robert D. Goodwin, entitled "A Simple Manostat of Constant Sensitivity," was published in the October issue of your JOURNAL without my knowledge because I would have been able to clear up a few points of difficulty mentioned by the author. I am presently engaged in preparing another paper on the Cartesian Manostat which I hope to publish soon in which a more thorough analysis of the theory will be made. Due to an oversight on my part I had failed to state in my first paper, under "Equilibriumof Buoyant Forces," that the area of the inner vent tube has been neglected. The suggestion made in Goodmin's note 3 to replace A2 by the internal area of the diver is not correct. I have already derived the equation in which the area of the internal vent tube is not neglected. The final equation after simplification and approximation may be written as (using the symbols of my paper' with the following additions: A, = cross-sectional area of inner vent tube, Vo= volume inside of float, and P. = pressure inside orifice, ~vhichmay be taken as nominally zero) :
It will be noted that when A. is small in comparison with A, then the above equation reduces to equation 8 of my paper. I do not think it is correct for Dr. Goodwin to state that the manostat has a constant sensitivity since this is only true when Vois made infinitely large. There is a much eimpler way of reducing the rate of change of sensitivity with pressure than by the method suggested by Dr. Goodwin. From the above equation this may be accomplished by increasing the'area of the inner tube where it comes in contact with the liquid seal and by making Al small. This in effect magnifies the volume inside the float. This particular design has been incorporated in an industrial type manostat which the Emil Greiner Company has recently developed. The suggestion is largely due to Dr. Teeters of Hoke, Inc. I should like to add that although the derivations of Dr. Goodwin may not be strictly rigid, I believe they have good pedagogical value.
' GILMONT, R.,Ind. Eng. Cham.. A n d . Ed., 18,633 (1946).
To the Editor: Thank you for the opportunity to comment on Dr. Gilmont's reply to the criticism which I recently published in your JOURNAL.I apologize for involving you as mediator in a polemic which might have been avoided had I not attempted so severely to condense my paper. In his letter of October 27 to you Dr. Gilmont indicates with reference to my third footnote that due to an oversight he had failed to state that the area of the inner vent tube has been neglected, i . e., assumed negligibly small, in which case A2 represents the inner area of the diver. Upon this assumption the analysis is certainly quite satisfactory. . Not wishing to write at length about an error which did not greatly affect the validity of Dr. Gilmont's conclusions, I, too, am culpable for having failed to show accurately the changes consequent to an understanding that Archimedes Principle is indifferent to any object immersed in the liquid uithin the diver. When Ax does not sufficiently represent the internal area of the diver Dr. Gilmont's equation immediately following equation ( 3 ) would, I believe, read:
where A, represents the area of the inner vent tube and P I the exhaust pressure expressed as height of liquid. The same equality may be obtained less equivocally, it seems to me, by considering the forces acting on the diver as follows: downward forces due to gravity and external gas pressure are W+P(A,+A2+As-a) d PI ad; the upward force on the bottom surface of the diver wall is (P+m)Aad, and that on the upper, inner surface of the diver is ( P - hl - hz)(A, A& The new design which Drs. Gilmont and Teeters propose will, I am sure, be an improvement relative to the modification suggested by me in that the size of the apparatus will not be so greatly increased. To avoid the necessity for thermost&ting the manostat I use a regulator akin to the U-tube design of my Figure 2 but replace the reservoir, N, by a simple levelling-bulb exposed to the atmosphere and filled with water or mercury as the pressure requires. For all but the lowest pressures this provides a manometer and pressure-adjusting mechanism as an integral part of the manostat.
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