Thnv. 



512 BRIDGE. 



The rise of Water produced by Obstructions to the Current, fyc.Continued. 



We have already admitted, that this Table is in- 

 complete, yet it will, in all probability, answer many 

 useful purposes. The science of hydraulics is as yet 

 so empirical, that we can seldom predict with cer- 

 tainty what will be the result of a proposed combina- 

 tion. It is probable that the fall or'head, and con- 

 sequently the velocity acquired, is always stated too 

 high, at least in the earlier part of the Table. For 

 the contraction of one fifth of the breadth, is nearly 

 as much as is observed in a narrow pipe. We have, 

 indeed, made no allowance for the contraction or di- 

 minution of effect which may be supposed to arise 

 from the friction and other causes in the original bed 

 of the river. Or, what is the same thing, the addi- 

 tional head which is requisite to overcome this fric- 

 tion, over and above that which is due to the assum- 

 ed velocity of the stream. And again, the friction 

 increasing under the piers, from the increased velocity 

 of the stream, will require also an additional head of 

 water to overcome it. This, in small velocities, and 

 with small obstructions, is a very great part of the 

 whole rise. Its proportion diminishes in the latter 

 part of our Table. So that, in all useful cases, it is 

 likely to be nearly counterbalanced by the great rate 

 of contraction we assume. 



In order that the Table should be complete, we 

 must divide it into two parts, one referring to the ve- 

 locity, and the other to the difference of level of the 

 river's surface, for a space equal to the breadth of 

 the bridge. The depth, too, is a material consideration 

 in discovering the acquired velocity. But we do not 

 see the importance of these minutiae, for the requisite 

 data are not to be obtained with similar exactness. 



As an example of the purposes to which this Ta- 

 ble may be applied, let us suppose that a bridge is to 

 be built over a river of 100 feet wide, the usual ve- 

 locity of which is 3 feet per second, and, of course, 

 the bed is in all likelihood composed chiefly of round 

 pebbles. Let these pebbles and gravel be supposed 

 to extend to the depth of 3 feet, and under that a 

 stratum of fine firm clay. Let it be proposed to 

 give the bridge a water-way of 75 feet, that is to 'say, 

 two abutments projecting 4^ feet each, and two 



piers of 8 feet thick each, a centre arch of 85 feet, 

 and two side arches of 20 feet span each. It is only 

 proposed to lay the foundations two feet below the 

 bed, and to spring the centre arch 2 feet above the 

 usual waters, giving it a rise of one-third of the span. 

 Let us inquire whether such a structure is likely to 

 be durable. 



From the Table it appears, that the obstruction 

 being one-fourth, and velocity 3 feet, the head will 

 be .2484-, or about 3 inches, and is therefore not 

 likely to encroach on the crown. But the velocity 

 under the bridge will be 5 feet per second, and, of 

 course, would require boulder stones or rock to 

 withstand it ; the gravel bed will therefore be cut up 

 under the bridge, and to a depth which, although 

 not easily predicted, is likely to be that which will 

 make the area of the section of the current, allowing 

 for contraction, as great as where the river is free. 

 For this will restore the original velocity, and pre- 

 vent farther damage, provided the pebbly stratum 

 holds to that depth ; for should the strata below be 

 harder or coarser the damage will be less, and if soft- 

 er the contrary. 



Suppose, again, the depth of the river, in its usual 

 tenors, to be 3 feet at the left, and 4- feet at the 

 right pier. Nothing is more common than such a 

 difference of depth ; and it is to be observed, that, 

 whatever may be the cause of the inequality, the 

 erection of the bridge does little or nothing to re- 

 move it. We may therefore suppose the inequality 

 of depth as likely to continue, whatever other changes 

 are produced. 



At left Pier. At right Pier. 



Original depth in feet .... 3 4-. 



Increase for obstruction, J . _1_. .... 1.33 



4. "5T33 



And 4- for contraction on the") , 



17 i hi..... l.3o 



above principle J _ 



New depth being as required 7 <- fififi 



velocity J 



Deduct original depth ... 3 4>. 



Depth cut by the river, in feet 2T . . . . 2.G6 



