THE TRANSPORTATION OF LIQUIDS 117 suction impellers are more complicated in design, and the water must be brought to the opposite side of the impeller through holes cored in the guide ring between the channels. As this may introduce a slight difference in pressure and cause an unbalanced axial thrust a small thrust bearing is provided. In the -single-stage pump two collars are merely placed next to the bearing to keep the impeller in place. FIG. 12. — Single-stage centrifugal pump with double-suction impellers. Hydraulic balancing devices secure perfect balancing, but they are only recommended for clean water. The single-suction impellers have wearing rings only on the suction side to prevent short circuit losses. The leakage from the last impeller enters the space between two discs one of which is fastened to the casing and the other to the shaft. Wearing rings on the periphery of these two discs prevent the leakage from escaping until a pressure is set up between the two discs to counteract the end thrust. This is also used on vertical pumps to support the part of the weight of the rotor that is not counterbalanced by the end thrust. Theory of the Centrifugal Pump. — The fundamental equation is ua = vr + 2 tan aa + •*• Ek + Or •*• 2 tan aa)2 where, referring to Figs. 9-10, ua — peripheral velocity, feet per second, vr = radial component of the absolute velocity waj aa = vane angle, degrees, g — 32.2 ft. per second, H — actual head pumped against, feet, Eh = hydraulic (or manometric) efficiency = actual head -r- ideal head, or Hg/(ua — q)ua, ua — q being the tangential component of the absolute velocity wa (see Fig. 9). Cf . " Hydraulic Efficiency" for values. In testing a centrifugal pump four sets of readings are taken: Capacity, Q; Head, H] Speed, N\ and Power, P. The observed test points are then plotted, and thus certain curves are obtained called the characteristics of the pump. Of these the HQ or Head-capacity curve is the