18 Jo.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



ti77 



ON THE TROPER DEPTHS BELOW WATER MARK Ot'' 



CILLS USED FOR DRAINAGE. 



By F. Bashforth, B. A., Fdlow of SI. John's Colkge, Cambridge. 



Engineers ;ire divided in llifir 0[)inions respecting; the proper 

 depllis I) 'low low water rn.irk at vvliieli llie cills of sluices, etn|iluyed 

 ill draiiiiiifj li.w land, ouglil to l)e jilaced. It appeals to me lliat a few 

 simple niailiem Uical consideralioiis will set tlie matter at rest. The 

 diftereiK-e lietweeii the densities of fre<h and salt water is well known ; 

 and from the aeknowledoed f ict that the tides flow up the bottom of 

 rivers, elevating the fresh water in their progress, and that large 

 livers, siieli as the Oronoco, at their monlhs, form inimense havs of 

 Jic^h water, the fresh water swimming on the surface — we learn that 

 tlie dill'crence of those densities is such as cannot be neglected. 



Let the figure represent a section of the water-gate 

 O A, cajiable of turning about O. Let the surfaces of the 

 fresh and salt water be at B ajid B' respectively, when 

 the momenta of the two pressures tending to turn the 

 gate equal 

 AM =x \ 

 A B' = X' ) 



O 



B 



O A = h 



B' 



P, I tlie density of the | ^'^^^^ \ water. 



/ = width of the sluice 



Pressure of the fresh water ou A B =: j p (/ A BJ 



A ='l'-2- 



Distance of cent, of press, below B=fBA= % x. 

 Moment of the pressure of the fresh water tending to turn the 



gate about O = i-^-Lf! (/,. 



Similarly, moment of the pressure of the sea tending to turn the 

 gate in the opposite direction = 



s p' I 



0-v)- 



These are supposed equal .' 



!-?i£%J_-^) — 'P'^"' 



or X^-ihx'^:=^(!c''-Zhx') (1.) 



.b^rLw i:^::r ,n::l^^ ^'" '^ ^ '^^^ '''='°-' -^ that O is H feet 

 .' = M.20and^ = J°3^^.^3 



a:= -3x 20.r= = 1.03 x 3G{6-60} 

 or;!;s _ GO a^ = 2002-32 

 It will be found on trird that ,r = G-1 feet verv nearly satisfies this 

 equa .on. ence we see that tl,e fresh water must be about! o a 

 oot Mgher than the sea water, when the tendency of the gate t"o turn 



undw:;r,'i:vnr"''-T'°-,- ^'^'"^"Sl" tl.is point would fr^equently be 

 lound worthy of consideration, it is not the most important. 



in 7i 1 • '"?'®, """ P''^«'"''''s of the /resh and salt waters at noints 

 .n the horizontal plane passing through A. Then we have ^ 



V 



100 X G-1 

 103 X 6 



GK) 



CIS 



tlie c. se,.instead of the fresh water rushing out the salt water would 



be' "ome'eirjal d""f '■ "T ""'f' ''T'' "' ''" <=■"• If tl'e fresh Taer 



he e^ll rthe wtl S'" f i'T ^''" '"'^'"'' "^ "'^ ^^^' ""-" =>» ^lo"g 



would be^eqnah ^'"' °^ "" "'""'"S) ^Le pressures of the twf 



low water mark-the point O being, as before, H feet above the sur- 



X' = 1 foot ) 

 /i =15 feet/ 

 . - . substituting in = ( 1) we get 

 *' -3 X 15 X- = 1-03{1 - 15} 

 = - 1-03 X 41 

 = -45-32 

 a = 1-02 ft.nearlv 

 . • . * - ,r' = 1-02 - 1-00 = -02 ft. = ^ foot. 

 In the first case we get 



X -x' = 6-1 - G ft. = ^ foot. 

 These examples are not supposed to belong to any particular ca'<e, 

 but it was necessary to make numerical applications of equation (1.) 

 to show clearly the result of calculatioj. We thus see that it is pos- 

 sible that the moment of the water lending to open the gates may be 

 greater than that tending to keep them closed, but that when the gate 

 Jiisl opeiix the pressure of the salt water in the same horizontal plane 

 with the cill must be greater than that of the fresh wafer in that plane ; 

 and consequently, at every orifice, below some point C, the salt will 

 flow inio the fresh water, and above that point the fresh water will 

 flow into the sea. In no case can B be less than about V- foot higher 

 than B', for in that case the moment of the pressure "of the fresh 

 water would be less thau that of the sea, and consequently the gate 

 would be closed. 



When there is a fall in a river of three or four inches per mile, it 

 becomes o( the greatest possible importance that not even one inch 

 should be throvpn away by an erroneously constructed sluice. It is to 

 such cases that this investigation is intended to applv. If the densi- 

 ties of the two waters had been the same, the lower'the cill the more 

 water would be discharged. 



OBLIQUE ELLIPTIC ARCHES. 



Sir— In the essay on Oblique Bridges by G. W. Buck, Esq., he con- 

 siders it not imperative on the engineer to erect oblique elliptical 

 arches, as they may generally be made segmental, and for that reason 

 has not considered the subject; as they sometimes are erected I send 

 you the following elucidation descriptive of a bridge of that form, of 

 siindiar dimensions to those over the line on the Edinburgh and Glas- 

 gow Railway, showing how it may be constructed according with his 

 scientific principles by converting the ellipse into circular arcs. If 

 you consider it worth the attention of your readers I will be obliged 

 by its insertion in your valuable Journal. 



Fig. 1. Development of elliptical arch crossing at an angle of 

 G0° 50'. A C D D' represents the skew of the bridge, and C F G D 

 its development; the line C K, to which the courses of the arch must 

 be parallel, should be theoretically at right angles to C F, but when it 

 does not suit the division of the courses it requires to be adjusted to 

 the nearer course, in this case it is made to join the seventh ; the 

 checks on the impost are at right angles to C D. 

 Fig. 1. 



