140 UNIVERSITY OF VIRGINIA PUBLICATIONS 



parallel to the axis? The theoretical limit being reached when AB = 2B, 

 in which case as it were the waves of disturbance sent out from the boundary 

 actually reach the axis and passing on expand to the boundary again, 

 whence they are again reflected, causing complete interference. Experi- 

 ments appear to be lacking to either settle this point or to justify further 

 speculation concerning it. 



10. In the foregoing we have spoken with special reference to pipes 

 under pressure ; there is no change to be made for straight regular conduits 

 flowing part full or regnilar straight open channels than to replace the 

 annular obstruction by a submerged dam of uniform height along the 

 sides and bottom of the cross-section, under which circumstances p becomes 

 the wetted perimeter and r the mean hydraulic radius or the area of the 

 cross-section divided by its wetted perimeter. H becomes the total fall of 

 the water surface in length L and in this ease is the same as li. 



II. DBTEEMINATIOiST OF THE CONSTANTS. 



11. The data for the determination of the constants in the formula 

 for the velocity of flow in pipes under pressure consist mainly of experi- 

 ments made on the sizes of pipes used for service in ordinary engineering 

 practice. The diameters vary from one-fourth of an inch to eight feet, 

 and the pressures are such that the velocities vary from one-tenth of a 

 foot to twenty feet per second. The main mass of experimental data is 

 confined to these limits in authentic and reliable experiments. WhUe the 

 range of the mean hydraulic radius from .005 to 2 feet is ample for pipes, it 

 goes up to 4 or 6 for conduits, and to the extreme limit of 75 for great 

 coastal plain rivers like the Mississippi. TTie conditions of regularity 

 and normal consistency with the theoretical principles are most nearly 

 realized in the class Imown in engineering practice as "new, clean, smooth 

 pipes.'" Tliis is a large class which in its differentiation consists of pipes 

 of tin (tin lined), zinc, lead, glass, galvanized iron, wrought iron or cast 

 iron coated with asphaltum or tar, wrought or cast iron pipes uncoated or 

 lined with cement, riveted wrought iron or sheet iron, coated and uncoated, 

 and pipes of wood, tile and earthenware. With this large variety of 

 inner surfaces, varying character of joints and projections there is a con- 

 siderable variety of roughness and consequently a considerable degree of 

 discrepancy in the tabulated results of different experiments. 



We shall first deal with the general class of "new clean pipes" as a whole 

 for a provisional determination of the constants and subsequently make 



