PROBLEMS 131 



from which A = 20.12, Vi = 6.21, and Vi^/lg = 0.60, so that the value of 

 H3 = 0.12 feet satisfies the formula. 



2. Measurements were obtained on a flash flood which flowed under a single- 

 track 5-pile trestle bridge 200 feet long. The percentage of obstruction was 

 14.5 per cent, and the bents were nearly in line with the current. The average 

 depth of the water downstream from the trestle, which was not clogged with 

 debris, was 4 feet. The observed fall through the trestle was 0.7 feet. What 

 was the discharge? 



First summarize the known factors. W2 = 200 - (200 X 0.145) = 171, 

 a = 0.145, D3 = 4, Hz = 0.7, and Di = 4.7. Substituting these values into 

 the D'Aubuisson formula, equation (1012), and using K = 0.96, we obtain 



Q =656^43.6+ Vi^ 



Assuming Vi^ = 40, a first trial Q = 656^83.6 = 6,000, from which 



£^ 6.000 ^ ^^^ ^^^^ 



Ax 200 X 4.7 



Assuming V^ = 41, second trial Q = 656V84.6 = 6,030, from which Vi^ = 

 41.2, by the same method. A third trial with Vi^ = 41.4 gives Q = 6,050, 

 Vi = 6.44, and Vi^ = 41.4, which checks. The class of flow should now be 

 computed to see if use of the D'Aubuisson formula is justified. 



F3= '■""> -7.56. i^ = 0.89, and . = »:?£ = 0.22 

 200 X 4.0 2g 4 



Entering Fig. 1004 with co = 0.22, and a = 0.145, the flow is seen to be in the 

 Class 2 area, not far from the Class 3 boundary. Yarnell's data indicate that 

 the Nagler formula is more reliable in this area. Substituting the given data 

 into the Nagler formula, equation (1011), and using K = 0.90 



Q = 1,233 4.00 - 0.3 y- Uo.70 + 1.47 



2g 



Using for V^jlg and V-^/2g the final values obtained in the D'Aubuisson solu- 

 tion, Q = 5,910. This is enough less than 6,050 to demand another approxima- 

 tion. Values of V^jlg and V-^/2g corresponding to Q = 5,910 might be used, 

 but in order to hasten the convergence of the successive trials, try Q = 5,700. 

 This gives Vz^/lg = 0.79, FiV2g = 0.57, and Q = 5,710, which is close enough. 

 The answers by the two formulas differ by about 6 per cent. The D'Aubuisson 

 formula was used first because it is more convenient. Since the flow is Class 2, 

 the result obtained using the Nagler formula is to be preferred. 



PROBLEMS 



1001. A rectangular flume 10 feet wide, of smooth concrete, must have a curve 

 with radius of about 200 feet and central angle of 40 degrees at the bottom of a long 



