GENERAL PRINCIPLES OF HYDRAULICS 471 
A few examples of the value of y are given below :— 
Character of the Wetted Surface, ¥ 
| Very smooth.—Smooth cement or planed wood dota ® ures. Gt) 0100 
| Smooth.—Planks, brick, or cut — < > ‘ ; : 0°290 
; h.—Rubble masonry F , ‘ ; oF ee 0°833 
| Very rough.—Ordinary earth canals iw Ween ete ‘ - | 2°B55 
412. Kutter’s Channel Formula.—Two Swiss engineers, Ganguillet 
and Kutter, devised a formula, generally known by the name of the 
latter, which has been largely used, notwithstanding the fact that it is 
somewhat cumbrous. The use of the formula is, however, facilitated by 
published tables. The formula is 
| 
41-6 4. 1811 4 0°00281 
. a ~ 900381 oft 
1+ (4 1-6 4.200 \ 
; a/m. 
where n is a coefficient depending on the roughness of the channel. 
A few examples of the value of ” are given below :— 
Character of Wetted Surface. n 
; Well planed timber . , , : 7 ; - | 0-009 
| Smooth cement, or coated clean pipes . ‘ - : ; - | 0010 
Rough planks , -| 0-012 
Ashlar, good brickwork, or fron pipes in ordinary condition ‘ - | 0013 
| Rough brickwork, or incrusted iron pipes . Pe PC 
Rough rubble in cement, canals in ae firm gray el. ; . - | 0°020 
Rivers or canals in good order . . d - - | 0°030 
413. Depth for Maximum Discharge in a Channel of Circular 
Section.—Let r= radius of section of channel (Fig. 767), and @ = angle 
_ subtended at the centre by the wetted perimeter. 
_ Assume that ¢ in the formula v=c ,/mi is constant for 
. different depths of stream. 
Wetted perimeter =r. 
| Area of section of stream = “(0 —sin ). 
CE ——_—_———— ae 
Therefore m= =2(2= ~ °), Fia. 767. 
And the discharge = "(0- sin 0)c er op Ni 
_ N(9—-sin 08 re 
JO ae 7" , 
The discharge will be a maximum when ora is a maximum. 
