In the case of a flight of m locks, a single boat in descending uses no more water than if there were only one lock, the same water passing from lock to lock, but in ascending it uses more. In the case of a number (2n) of boats going up and down alternately (case 5), the lockage is m n L, the lockage per lock per boat being followed by an equal train ascending (cases 7 and 8), the lockage is less. If n is supposed to be equal to m, the average lockage per boat is as follows:—
| m | = | 1 | 2 | 3 | 4 | 5 | 6 | Infinity |
| Lockage per boat | = | L̲ 2 | L | 7̲L̲ 6 | 5̲L̲ 4 | 1̲3̲L̲ 10 | 4̲L̲ 3 | 3̲L̲ 2 |
Thus in a case where n and m are very large, the average lockage per boat, when the boats pass up and down in trains, is to the lockage per boat, when the single boats pass up and down alternately through m single locks all at different places, as 3 is to m. The reason for the difference, which may appear puzzling, is that when the locks are at different places they are worked independently of one another.
Sometimes a lock is provided with intermediate gates which provide a short lock for short vessels. In the Manchester Ship Canal, alongside each lock there is another of smaller size to be used for small vessels and thus save lockage. At the Eastham lock, where the Manchester Ship Canal descends into the estuary of the Mersey, there is, below the tail gates, an extra pair of gates opening towards the estuary, so that the lock can be worked when the water of the estuary is higher than that in the canal. Water can be economised by means of a “side-pond,” into which the upper portion of the water from a lock can be discharged and utilised again when the lock has to be filled. If two locks are built side by side, each acts as a side-pond to the other. Two flights of locks can be built side by side.
Sometimes instead of a lock there is an inclined plane, up or down which are drawn on rails caissons containing water in which the boats float. The rails extend below the water-levels of the two reaches, and the caissons can thus be run under the boats. “Lifts” have also been constructed by which the boats can be lifted bodily and swung over from one reach to the other.
4. Other Artificial Channels.—The method of calculating the discharges of channels in which water is to flow is a question of hydraulics. The principles and rules to be followed, in the design of earthen channels, have been stated in [Chap. IV., Art. 6], and in [Chap. VIII., Art. 5]. The design of banks has been dealt with in Art. 1 of this Chapter. For conveying water for the supply of towns, or for other purposes, masonry conduits are often used. A usual form is shown in [fig. 30]. The curving of the profile of the cross-section gives an increased sectional area and hydraulic radius, and hence an increased discharge.
Fig. 30.