THE FLOW OF WATER UNDER PRESSURE.

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pipe will have a higher colunm standing in it than is the casewith the tuhe which is placed over a contracted length. Forinstance, on fig. 1 the sectional areas at E and P are thesame, and the areas at C and K are also equal to each other,but are smaller than those at E and P, whilst the area at I is thesmallest of all. Disregarding the slight loss of head due tofriction, the level to which the fluid rises at the variouspoints is indicated by the heights ED and PQ, CH andKN, and IJ. Fig. 2 shows similar results, equal sectionalareas producing equal pressures, and consequently equalheights. In other words, a pipe filled with water, and sub-jected to a head, has a greater pressure in it when thewater is at rest than when the water is in motion; again, it hasa greater pressure when the velocity is checked by an enlarge-ment in the pipe, and has a less pressure when the velocityis accelerated by a reduction in the pipe. This has beenexpressed by Professor Cotterill thus:—If Z — the elevationor actual head for any section of the pipe, p = the pressure,u = the velocity, W = weight of a cubic foot of water, then

— + + Z = constant,

2g W

and he describes the first term of this equation as representing“ energy of motion,” the second “ energy due to pressure,” thethird “ energy of position,” the total energy of the water thusbeing shown to remain constant as it traverses the pipe(frictional resistance not being considered). If the friction ofthe fluid be taken into consideration, some of the head wouldbe lost, and this loss produces what is termed the hydraulicgradient, as is shown by fig. 3.

Where a current of water is passing at a high velocity froma large pipe through a small opening or valve, a loss of usefuleffect follows. In the case of water flowing through a contrac-tion (such as it meets with in valves), there is a practical loss ofthe head which existed in the main before the water entered thevalves on the way to the cylinder. The head which inducedthe acceleration of velocity does not all re-appear upon the