Theory. 



514 BRIDGE. 



The Rise of Water produced by Obstructions to the Current, cj-c. Continued. 



The 



Velocity. 



Description of Hirer. 



Obstructions. 



Per Sec. P. Hour, 

 Ft. In.' Miles. 



The Current 



usually termed 



The Bottom, 



v.hich just bears 

 such velocities 



_ Head of 



Head'! VeL~~| 



water, and velocity produced at the obstruction in feet. 

 ' ~liJad.~ Vei. 



.0162, 1.05 



Head. Vel. Head. Vel. 



$ or 3 

 ior6 

 I. 

 II. 



III. 

 IV. 



V. 



VI. 



X. 



14 

 2 T ' T 



Dull 



Gliding 



Smooth 



Uniform tenors 



\ Ordinary / 

 " Freshes ( 



TExtraor- 

 ] dinary 

 j Floods 

 f and rapids 



Torrents and 

 cataracts 



Ouse and mud 

 Soft clay 

 Sand 

 Gravel 

 Pebbles 

 Shivers and 



chingle 

 Boulders and 



soft schistus 

 Stratified 



rocks 

 Indurated 



rocks 



.0014- 

 .0058 

 .02 jl 

 .0924- 

 .2079 



.3696 



.5775 



.8316 



2.3100 



.394; 



.787 

 1.575 

 2.75 

 4.325 



5.5 

 7.875 

 9.45 

 15.75 



.0033 

 .0133 



.0532 

 .2128 



.4788 



.52 

 1.05 

 2.1 

 4.2 

 6.3 



.0067 

 .0267 

 .1069 

 .4276 

 .9621 



.8412 8.4 

 1.3200^0.5 

 1.9152 '12.6 

 5.320 21. 



.7 

 1.4 

 2.8 

 5.6 

 8.4 



11.2 



14.0 



1.7104 

 2.6725 

 3.848416.8 

 10.69 28. 



.0617 

 .259 

 1.036 

 2.331 



4.144 

 6.475 

 9-324 

 25.9 



2.1 



4.2 



8.4 



12.6 



16.8 

 21.0 



25.2 

 42. 



.068 



.274 

 1.0S6 

 4.344 

 9.77425 



2.1 

 4.2 

 8.4 

 16.8 

 i.2 



17.37633.6 

 27.15042. 

 39.09650.4 

 108.6 84. 



By the help of this Table, we may see the effects 

 likely to be produced in rivers by the usual acci- 

 dents to which they are liable. The velocities above 

 ten feet produce inuadations that sweep away every 

 kind of structure. Those in the latter part of the 

 Table are given as fair results of the theory, but, in 

 fact, they are impracticable. 



In Westminster Bridge, the piers form about one- 

 sixth of the water-way ; the velocity is between 2 

 and 3 feet, or more accurately 2- feet ; the head, 

 therefore, will be between .036 and .082, more accu- 

 rately .045, or about half an inch ; which is exactly 

 the greatest fall observed by Labelye. 



At London Bridge, the apparent water-way is on- 

 ly one-fourth of the breadth of the river, but is much 

 reduced by the drip shot piles, which have been dri- 

 ven into the bed to protect the foundations. The ve- 

 locity of the stream nbove the bridge is 3 feet 2 inches, 

 which, by this Table, would give a head of 2.6 feet, 

 and by the former one 4 feet. We cannot suppose 

 these piles to take off less than one fifth of the wa- 

 ter-way, which would make the head 4.31 by this 

 Table. But probably the contraction is greater than 

 this Table supposes, coming nearer that assumed in 

 the former, (which would have given us a head of 

 almost 6 feet,) since a fall of 4 feet 9 inches was ob- 

 served about the year 1730 ; and the excavation had 

 become so very dangerous, as to suggest the mea- 

 sure of cutting out one of the piers of the bridge, 

 and throwing two arches into one. 



The fall at Blackfriars will be somewhat less 

 than at Westminster, but will not exceed one inch. 

 In the same example, as before tried, this Table af- 

 fords the following results : 



1 st, The Bridge in common Waters. 



Original depth 3 4 



Obstruction 1 1.3? 



4 5.3 

 Contraction -^ 2 2.^ 



4.2 5.6 



Original depth 3 .... 4 



Depth cut by the river .... 1.2 .... 1.6 

 So that the piers are safe in common waters. 



2d, The Bridge in Floods. 



General depth 6 



Add for obstruction , or 3.75 



9.75 

 Contraction T V 487 



Depth when general velocity restored,! o 137 



viz, 5 feet per second J 



Add f to bring it to terror velocity . . 6.092 



The pebbly stratum will be cut untill . 



the depth is j 



But there is only 9. 



There will be cut below the bed 



6.23 



Now, since the pebbles extend only to three feet, 

 the waters pass to the clay, which bears only one- 

 third of this velocity, and would therefore require a 

 depth of 45.69, or 36.69 below the bed : The bridge 

 therefore cannot stand in such floods as this. Sup- 

 pose, then, that it be proposed to make a total change 

 of foundation, as, by paving all across the river, or 

 any similar operation, referring to the Table with an 

 obstruction of , and velocity 5 feet, we find the- 

 6 



