number and the velocity of current, called the rating of the instrument, is usually effected by drawing the meter at a given speed through still water. The parts is a rudder and the part B a ballast for use in very deep water. The approximate mean velocity of flow at a cross-section of a stream may be determined by measuring the velocity of the depth at .6 below the surface at the deepest part of the cross-section. When accurate results are required, measurements should be taken at different parts of the section as well as at different depths of the same section and the average calculated. The ordinary method of procedure is as follows:

A range at right angles to the stream is selected (see Fig. 2) and divided into any desired number of parts. Soundings are taken along the points of division, and at the same points the

mean velocities are determined by moving the meter vertically at a uniform rate from the surface of the water to the bottom. and back to the surface. The mean velocity of a division. multiplied by the corresponding area gives the partial discharge of that division. The sum of the partial discharges is the total discharge of the river.

Determination of Discharge by Floats.-The discharge of streams is best determined by means of rod floats, which are wooden or hollow tin cylinders weighted at the lower end. They should be placed as near the bottom of the stream as possible. A suitable portion of the stream between two cross-sections at right angles to it is selected." The sections are divided into a suitable number of parts, soundings are taken at each division

point, and the float is timed between the corresponding division points. The partial areas of the two cross-sections are determined, and the mean of the areas of the corresponding division multiplied by the corresponding velocity will give the partial discharge of that division. The sum of the partial discharges is the total discharge of the river.

The mean velocity as observed by a rod float is to be taken as the actual mean velocity only when the float is made to pass close to the bottom. When the float is immersed only to a

depth i, the actual mean velocity is,

in which Vm is the measured mean velocity and d the depth of water at which the measurement was taken.

When a surface float is used, the actual mean velocity may be obtained approximately by multiplying the measured mean velocity by .8.

FLOW OF WATER IN PIPES

In determining the flow of water in pipes, the discharge in cubic feet per second is Q= .7854d2v, in which dis the diameter of the pipe in feet and v the actual velocity, in feet per second. The theoretical velocity is v√√2gh, h being the static head. This head h, which is available before the flow begins, sustains losses during the flow due to skin friction between the water and the pipe, to resistances at entrance, to bends and elbows, and to other causes, resulting in a reduction of the theoretical velocity. The actual velocity is,

in which I is the length and d the diameter of the pipe, both in feet; f, the coefficient of resistance for friction; and c, the sum of all coefficients for losses due to entrance, bends, valves, etc. For a pipe whose length is more than 1,000 times its diameter, called a long pipe, the value of 1+c is very small in comparison

with the loss due to friction and is therefore neglected. The

formula used for long pipes, is v=

2ghd
fl

The value of ƒ depends not only on the roughness of the pipe, but also on its diameter and the velocity of flow. Its values for a smooth pipe are given in the preceding table. For rough pipes, these values should be multiplied by 2.

COEFFICIENTS FOR ANGULAR BENDS
(a= angle of bend in degrees)

a 10° 20° 40° 60° 80° 90° 100° 110° 120° 130° 140° 150°

k, .017.046.139.364 .74 .984 1.26 1.56 1.86 2.16 2.43 2.81

When the pipe is shorter than 1,000 diameters and the first

of the preceding formulas is used, the component parts forming the value of c must be ascertained and the results added and substituted in the formula. The coefficient ks for angular bends can be taken from the accompanying table giving its value for different angles. The coefficient for

circular bends is ce

a

180

kc, in which a is the angle

of the bend and ke is a constant depending on the ratio of the radius of the pipe to that of the bend and is given in the following table for circular bends.

COEFFICIENTS FOR CIRCULAR BENDS
(r=radius of pipe. R=radius of bend)

ke .131.138 .158 .206 .294 .440 .661 .977 1.408 1.978

Valves. With reference to the accompanying illustration, the coefficients of resistance j for different ratios of b to d are as follows: