A Treatise On The Principles And Practice Of Dock Engineering

DURATION OF LEVELLING OPERATIONS. 257 Duration of Levelling Operations.—It is often désirable to know how Ion- it will take to level up a lock from a lower to a higher level through the medium of a culvert. If the source from which the water for the purpose is drawn be maintained at a constant level, or so nearly constant as to be conceivably treated as such, the calculation is a simple one. The theoretical velocity is u = 8 7 A, as previously explained. This multiplied by the sectional area of the culvert, or of the culverts if there be more than one, combined with a suitable coefficient of discharge, gives the quantity of water passing in unit time, whence the total time is obtained by dividing into the quantity of water required to Hll the lock. Therefore, algebraically, the time in seconds, 8acjh’.....................(42) where Q is the quantity required in cubic feet, a the culvert area in square feet, and c the coefficient of discharge—varying from -5 to -6, according as the culvert is long or short. If the source of supply be not maintained at a sensibly constant level during the process of filling, as when two docks, whose areas are not very excessively unequal, have to be brought to a common level by inter- communication, a suitable formula may be deduced from the same principles as follows :— In addition to the previous notation, let At and A3 represent the areas of the docks in question, hT the height by which the lower dock (Aj is raised, and h2 that by which the higher dock (A,) is lowered. Then Äj + h2 = h. Ilie initial velocity of intlux is 8 J h, the final velocity is zéro; the mean velocity, therefore, is 4 74. The rate of influx thus becomes 4 acjh. The quantity of water required to be transferred is, indifferently, Aj Ä, or A2 Åg—that is, -A] ^1 ~ "^2 ^2> but h^h-h,. Therefore Ax^ = A2 (Ä - hx), or ^(^1 + A2) = A2Å. Thät is, Substituting this value for /^ in A, hv the quantity of water required to be transferred (Q), and completing the equation as in the previous example (42) we finally obtain— r ' ’ -A-1 Ag Jh <~ÅrTA;x4"^...........................(43) Throughout the remarks which have been made in connection with structural operations it has been found convenient to use the word Lock as a more or less generic term to inelude Entrance and Passage as well. 17