The quantity _f_ is sometimes called the “friction factor.” For smooth, new pipes from 4 feet down to 3 inches in diameter its value may be taken from .015 to .03. An approximate mean value may be taken at .02. The last member of equation (8) is Chezy’s formula, and it is one of the most used expressions in hydraulic engineering. Some values for the coefficient _c_ will presently be given. The quantity _r_ found by dividing the area of the cross-section of the stream by the wetted portion of its perimeter is called the “hydraulic mean radius,” or simply the “mean radius.” The other quantity, _s_, appearing in the formula is, as shown by the figure, the sine of the inclination of the bed of the stream. In order to determine the discharge of any pipe, conduit, or open channel carrying a known depth of water, it is only necessary to compute _r_ and _s_ from known data and select such a value of the coefficient _c_ as may best fit the circumstances of the particular case in question. The substitution of those quantities in Chezy’s formula, i.e., equation (8), will give the mean velocity _v_ of the water which, when multiplied by the area of cross-section of the stream, will give the discharge of the latter per second of time. It is customary to compute _r_ in feet. The coefficient _c_ is always determined so as to give velocity in feet per second of time. Hence if the area of the cross-section of the stream, _a_, is taken in square feet, as is ordinarily the case, the discharge _av_ will be in cubic feet per second. [Illustration: Progress View of Construction of New Croton Dam.] =187. Kutter’s Formula.=—The coefficient _c_ in Chezy’s formula is not a constant quantity, but it varies with the mean radius _r_, with the sine of inclination _s_, and with the character of the bottom and sides of the open channel, i.e., with the roughness of the interior surface of the closed pipe. Many efforts have been made and much labor expended in order to find an expression for this coefficient which may accurately fit various streams and pipes. These efforts have met with only a moderate degree of success. The form of expression for _c_ which is used most among engineers is that known as Kutter’s formula, as it was established by the Swiss engineer W. R. Kutter. This formula is as follows: ( 1.811 .00281) ___ ( ------ + 41.65 + ------) √_r_ ( _n s_ ) _c_ = ---- (------------------------) _n_ ( ___ ) ( √_r_ .00281 ) ( ----- + 41.65 + ------ ) ( _n s_ ) The quantity _n_ in this formula is called the “coefficient of roughness,” since its value depends upon the character of the surface over which the water flows. It has the following set of values for the surfaces indicated: