6 BULLETIN 194, U. S. DEPARTMENT OF AGRICULTURE. 



The general equation for the slope, includmg this correction is 



' s^ h-(h^-K,) (Q^ 



where hyg equals the velocity head, in feet, necessary to create the 

 mean velocity at the lower end of the reach, and hyi equals the velocity 

 head of the mean velocity at the upper end of the reach, while s, h, 

 and L have the same significance as shown on page 2. For example, 

 involving this correction see page 15. 



In addition to the cross sections spoken of above, the field data 

 necessary to determine the hydraulic grade is an accurate determina- 

 tion of the length of the reach, L, in feet and of the difference in ele- 

 vation, or fall, h, in the surface of the water between the upper and 

 the lower ends of the reach, in feet. 



By far the greatest opportunity for error lies in the determmation of 

 the fall. In order to obviate inaccuracies due to shght local changes 

 of surface slope a reach should be chosen of sufficient length that a fair 

 average surface slope may be determined, yet it should not be so long 

 that distinct changes in gTade may greatly change the mean velocity 

 throughout the reach. In the experiments conducted by the writer 

 and his associates 1,000 feet was assumed as a fair length to be tested. 

 It is impracticable to make an extended series of measurements and 

 install the equipment necessary to carry a water level through pipes 

 between the two ends of the reach, therefore, whatever method is 

 used for the actual determination of the level of the water surface at 

 the ends of the reach, the difference in elevation between the bench 

 marks at the ends must be determined with a spirit level. 



The error wiU approximate a constant quantity for a given 

 length. Assume an allowable error in feet for careful work of 

 0.017Vdistance in miles. ^ For length of reach of 1,000 feet the allow- 

 able error would thus be 0.0074 feet. A grade of 0.0074 per 1,000 

 feet would be 0.04 foot per mile. The allowable error for a reach 

 1,000 feet long would thus be 4 per cent of the grade of a canal 

 having a fall of 1 foot per mile. The error in the determination of 

 the surface slope thus has a great deal more influence on the value of 

 n for low gradients (used in connection with large canals in earth 

 sections) than it does for the steep gradients commonly used for 

 irrigation canals. 



The value of V, the velocity, in feet per second, is found by the 

 formula 



V=S (10) 



The discharge, Q, in cubic feet per second, is determined by a direct 

 m.easurenient in the field, by weir or current meter. The discharge, 



1 Precise Leveling. In Topographic Instructions of the U. S. Geological Survey, 1913, p. 100. 



