6 BULLETIN 194, U. S. DEPARTMENT OF AGRICULTURE. 
The general equation for the slope, including this correction is 
s= h-(h -h yi ) 
where h T2 equals the velocity head, in feet, necessary to create the 
mean velocity at the lower end of the reach, and h vl 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 determination of 
the fall. In order to obviate inaccuracies due to slight local changes 
of surf ace 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 grade ma}- 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 will approximate a constant quantity for a given 
length. Assume an allowable error hi feet for careful work of 
0.017Vdistance in miles. 1 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=| (10) 
The discharge, Q, in cubic feet per second, is determined by a direct 
measurement in the field, by weir or current meter. The discharge, 
i Precise Leveling. In Topographic Instructions of the U. S. Geological Survey, 1913, p. 100. 
