1136
THEORY AND PRACTICE OF ENGINEERING.
Book II.
If the surface GII, in fig. 1726., be placed at a certain distance E I from the orifice E, thewater in escaping, acquiring a new degree of velocity in going through the space E I, will
Fig.1725.
Fig.1726.
give a greater shock than in the preceding case, because its velocity will then be expressedby the root of its height FI; whence it has been imagined that the impact should be equalto the weight of a column having the orifice E for its base, and the line FI for its height,without remarking that, although the velocity of the water does really increase, yet thequantity which would leave the reservoir would be always the same, at whatever distancethe surface might be situated ; thus a greater force has been calculated on in workingmachinery than really existed.
Another supposition was that, if the water were directed by a pipe I E F L, its impactmight be expressed by the weight of a column IK PE, but it is not possible that thistube should fill perfectly, since, whatever its length, the velocity of the water at itsissue would always be greater than at its entrance; consequently a column could not beformed without being increased by the acceleration, unless it were so narrow that itsvelocity would be more retarded by friction than it could be increased by the acceleration ;for the water in the reservoir being alone capable of maintaining the column E K P F,that in the tube not being replaced by the sides, its discharge could not be greater thanthat of the orifice which fed it.
When the velocity of the impact of water is accelerated, it is equal to the weight of acolumn having for its base the surface struck, and a mean proportional between the heightof the water in the reservoir and the line which expresses the elevation of its level abovethe surface struck for its height; consequently the greater the interval between the surfaceand bottom of the reservoir, the more power will be gained to work a machine, showingthat the only advantage to be drawn from the tube E L is to direct all the water towardsthe surface, and prevent it from being dissipated in passing through the air.
If a prismatic reservoir BCDE be continually filled with water, and a rectangularorifice F G III be made in one face E C, serving as the entrance to a canal whose bottomand sides are composed ofrectangles FIX S, I H V X,
F G T S, and a power IIsustaining a vertical surfaceNOMQ equal to the rec-tangular aperture, and thisbe suddenly opened, theimmovable surface will bestruck by a force equal tothe pressure which sustainedthe sluice when the aperturewas closed; that is to say,the impact will be equal tothe weight of a prism ofwater, having the surfacestruck for its base, and themean height LK betweenLa and L b for its height.
This is evident, for thevelocity of the water in thecanal being uniform, andexpressed by the root of the mean height LK, the impact will be equal to the product ofthis surface multiplied by the square of a/LK, or, which is the same thing, by LKitself: consequently, if the opposite surface contained 4 square feet, and the mean LK10 feet, the impact would be equal to the weight of 40 cube feet of water, or about 3150lbs., which is the force required by the pow’er R to support in equilibrio the impulse of a