In addition to the disc friction there is also a small amount of friction between the water and the interior of the runners, due to the outward flow of the water through the wheel passages. This, however, is negligible compared to the disc friction.

Capacity of Centrifugal Pumps.-When the velocity of flow V, through the runner of a centrifugal pump is known, the quantity of water passing per second can be readily obtained by taking the product of this velocity and the circumferential area of the passages through the runner; or, if the velocity of whirl in the volute V, be known, the quantity passing can be found from the product of this velocity and the sectional area of the volute close to the discharge pipe, which is usually made equal to the area of the discharge pipe itself. Whence from a knowledge of the dimensions of a pump both V, and V, can be readily obtained for any given discharge. The most important quantity to obtain is, however, the speed of the pump V for any given discharge. Expressions have already been given for V in terms of the head H, the angle 6, the velocities V, and V.; but on comparing the value of V calculated from these expressions with actual values, a discrepancy will be discovered which is largely due to the friction of the water in the suction and discharge pipes, and in the pump itself. The latter quantity can be most readily expressed in terms of the length of pipe, which produces an equal amount of friction. A few cases that the author has examined appear to show that the internal resistance of the pump and foot valve together is equivalent to the friction on a length of about 80 diameters of the discharge pipe. This head must be added to the actual lift of the pump in order to find the real head H, against which the pump is lifting.

When designing centrifugal pumps it is usual to make the velocity of flow V, about 2gH, and the diameter of the runner about twice the diameter of the "eye," the latter being usually equal to the diameter of the discharge pipe.

A concrete example of a pump in which the actual performances are known, will serve to show the extent to which our theoretical deductions may be trusted.

The pump is fitted with a volute, but no whirlpool chamber or bell-mouth.

The curves in Fig. 613 show in more detail the actual results obtained from this pump.

Multiple-lift Centrifugal Pumps.-In the case of a centrifugal pump which delivers against a very high lift, the peripheral speed of the runner becomes very great, and the skin friction of the discs assumes somewhat serious proportions. The very high speed of the runner is not a serious drawback for pumps driven direct from steam turbines or electric motors, and, in fact, such speeds are often found to be very convenient; the angle 0, however, becomes inconveniently small, and the skin friction is often so great as to materially reduce the efficiency. In order to avoid these drawbacks and yet obtain high lifts, two or more pumps may be arranged in series. The first pump delivers its water into the suction pipe of the second pump, which again delivers it to the third pump, and so on, according to the lift required; by this means the peripheral speed and the disc friction can be kept within moderate limits. One of the earliest and most successful pumps of this type is the Mather-Reynolds pump, made by Messrs. Mather and Platt, of Manchester, and by whose courtesy the section shown in Fig. 613a is reproduced.

The direction in which the water flows through the pump is indicated by arrows. It enters the runner axially from both sides, in order to eliminate axial thrust, and after traversing the runner the water is discharged into a chamber fitted with

expanding guide-passages for the purpose of converting the kinetic energy of the water leaving the runner into pressure energy. This chamber is the special feature of the pump, and judging from the excellent results obtained, it much more

effectually produces the desired result than the ordinary whirlpool chamber mentioned in a previous paragraph. The reader should also notice the great care that has been bestowed on the design of the pump, in order to avoid sudden changes in the direction of flow, and in the cross-section of the passages.

In Fig. 6136 is shown a multiple chamber pump of the same design. The water in this instance enters on one side only of the runner; then, after passing through expanding guidepassages, it is brought round to the other side of the runner, and after passing more guide-passages, it goes on to the next runner, and so on.

The following results of a test of one of these pumps will serve to show what excellent results are obtained; the figures are taken from curves published in the maker's catalogue :

The following results of a test by the author on a multiple Parsons centrifugal pump, driven direct from one of their steam turbines, may be of interest :—