Kirby v. Gay

Houkbn, J., delivered the opinion of the court. This appeal is from a decree of the chancery court of Harrison county, in which the chancellor adjudicated the [785] size of pipe that the appellee should have, in order to receive one-fourth of the water produced by an artesian well. There is no question of law presented by the facts in this record, since the parties litigant seem to have agreed as to their mutual rights in the premises, in so far as being entitled to receive water from the well in question is concerned, the only question left for decision being what size of pipe must be used, under existing conditions, to correctly distribute the water afforded by the'well, in the proportion of three-fourths to the appellant and one-fourth to the appellee. The chancellor reached a conclusion in his decree which we do not think can be sustained by the facts in evidence, since the solution of such a question must necessarily depend upon certain well-established, scientific facts and rules, the result of which is influenced by other collateral facts, such as are not disclosed by this record. As we see it, the depth of the well, the size of the well, the variation in the size of the pipe between the source of the flow and the point of discharge, are not material to the issue, as we think the capacity of the well, and the size of the pipe at the point of discharge, have remained constant, and, therefore the propórtion in which the water actually produced is distributed is the sole question for determination in this case. The well-recognized rule for determining the relative capacities of pipes is: ‘ ‘ The capacity of one pipe is to the capacity of another pipe as the square of their radii. ’ ’ This rule is deduced from, the equally well-established and recognized rule that “the capacity of a pipe is determined by the area of the circle described by a cross-section of the pipe,!’ and, since the area of a circle is pi (3.1416) times the radious square, then the correctness of the rule first announced for establishing the relative [786] capacity of two pipes conforms to this same theory, and will always result in practice, as correctly admitted by the witnesses for both the appellant and appellee in the lower court, in a pipe of a given diameter discharging’ one-fourth as much, liquid under the same pressure as another pipe of twice the diameter of the- first one. When the foregoing rule is considered, together with “Pascal’s Law,” which is, “Liquids transmit pressure equally in all directions, and this acts. at right angles upon the surface pressed,” then it is at once apparent that the proper way to determine the relative amount of water discharged at a given point under a given pressure must be determined by the relative size of the pipes through which the water is to be discharged. If the question here presented only involved the distribution of the water discharged into open vessels, then the solution would be simply that a pipe one arid one-fourth inches in diameter would discharge one-fourth of the water flowing through a pipe two and one-half inches in diameter, when the 'point of discharge was of equal elevation, and met with the same resistance; but, since the resistance to be overcome by the discharged water as indicated -by the record, consists of pipes conducting the water' into the residences, and probably other parts of the premises - of the litigants, then the rules herein. announced would vary in their application according to the relative resistance to be encountered by the separate streams discharged from the well, such as relative elevation of discharge, etc. This" record does not 'disclose these important additional facts, and therefore neither the chancellor hop ¡this court could reach -a correct conclusion on this question without the aid of this additional information, and therefore the cause is reversed, and remanded for a new trial, in order that these important additional facts may be .ascertained, and a decree rendered in accordance with [787] tlie rules hereinbefore announced,'as applied to tbe conditions as they may exist, or as contemplated in tbe use of the water by the respective parties. Reversed and remanded.