478 HYDROMECHANICS [HYDRAULICS. ing chamber to a fixed level marked on the wall of the chamber. When adjusted it is locked. Let ia 1 be the area of the orifice through the sluice at A, and o> 2 that f the fixed orifice at B ; let ftj be the difference of level between the surface of the water in the canal and regulating chamber ; h z the head above the centre of the discharging orifice, when the sluice has been adjusted and the How has become steady; Q the normal discharge in cubic feet per second. Then, since the ilow through the orifices at A and B is the same, Q = f lWl V2<//( 1 = c 2 a V-20/t 2 , where q and c$ are the coefficients of discharge suitable for the two orifices. Hence cii = // Ca V
- 1
Suppose now that in the interval between the visits of the canal officer the level of the canal rises h feet, causing the heads relatively to the orifices A and B to become h[ and h %. Since the areas of the orifices are unchanged and therefore or the ratio of the effective heads above the orifices A and B is un affected by the change of level of the canal. Also Eliminating h(, we get ij + h. 2 - and the dischare in the altered conditions is That is, Q; = /Vrj Q V V + h Height of Oriflce. Width of Oriiiee. Head above top edge of Orifice. Discharge per sec. in e. feet. Canal Lodi 1 12 0-12416 32 6165 Canal of Cremona T31816 0-131 131 7"5 Sardinian Module . 0-6562 G 6562 6 r 6 2"046 Oncia Magistrate of Milan 0-655 0-3426 0-3294 0-866 In the most elaborate Italian modules the regulating chamber is arched over, and its dimensions are very exactly prescribed. Thus in the modules of the Naviglio Grande of Milan, shown in fig. 69, the measuring orifice is cut in a thin stone slab, and so placed that the discharge is into the air with free contraction on all sides. The adjusting sluice is placed with its sill flush with the bottom of the canal, and is provided with a rack and lever and locking arrange ment. The covered regulating chamber is about 20 feet long, with a breadth l - 64 feet greater than that of the discharging orifice. At precisely the normal level of the water in the regulating chamber, there is a ceiling of planks intended to still the agitation of the water. A block of stone serves to indicate the normal level of the water in the chamber. The water is discharged into an open channel 655 feet wider than the orifice, splaying out till it is 1 637 feet wider than the orifice, and about 18 feet in length. This ap paratus was invented in the 16th century, and is still ustd. The greatest objection to it is the loss of level between the canal and discharging channel. Arrangements precisely similar to an Italian module are in use in England, for discharging compensation water into streams from impounding reservoirs. The fullest account of Italian modules is to be found in Colonel Baird Smith s Italian Irrigation. 55. Spanish Module. On the canal of Isabella II., which supplies water to Madrid, a module much more perfect in principle than the Italian module is employed. Part of the water is supplied for irriga tion, and as it is very valuable its strict measurement is essential. The module (fig. 71) consists of two chambers one above the other, the upper chamber being in free communication with the irrigation canal, and the lower chamber discharging by a culvert to the fields. In the arched roof between the chambers there is a circular sharp edged orifice in a bronze plate. Hanging in this there is a bronze plug of variable diameter suspended from a hollow brass float. If the water level in the canal lowers, the plug descends and gives an enlarged opening, and conversely. Thus a perfectly constant dis charge with a varying head can be obtained, provided nf clogging or silting of the chambers prevents the free discharge of the water or ^__^__^_^ _ the rise and fall of the float. I.I, r-JsP The theory of the module is very simple. Let R (fig. 70) be the radius of the fixed opening, r the diameter of the plug at a distance h from the plane of notation of the float, and Q the re quired discharge of the module. Then 0-63, If the orifice at B opened directly into the canal without any intermediate regulating chamber, the discharge would increase for a given change of level in the canal in exactly the same ratio. Con* sequently the Italian module in no way moderates the fluctuations of discharge, except so far as it affords means of easy adjustment from time to time. It has further the advantage that the cultivator, by observing the level of the water in the chamber, can always see whether or not he is receiving the proper quantity of water. On each canal the orifices are of the same height, and intended to work with the same normal head, the width of the orifices being varied to suit the demand for water. The unit of discharge varies on different canals, being fixed in each case by legal arrangements. Thus on the Canal Lodi the unit of discharge or one module of water is the discharge through an orifice 1-12 feet high, 12416 feet wide, with a head of 32 feet above the top edge of the orifice, or 88 feet above the centre. This corresponds to a discharge of about 6165 cubic feet per second. Two modules would be the discharge of a similar ori fice of twice the width. The following table gives some examples of different units of discharge. Choosing a value for E, successive values of r can be found for different values of h, and from these the "* j~R ^ -a? - V! Fig. 70. curve of the plug can be drawn. The module shown in fig. 71 will
discharge 1 cubic metre per second. The fixed opening is 2 metre
