Determination of flow surface profile imperfection allowing hydraulic drop at mid section of contraction

Determination of flow surface profile imperfection allowing hydraulic drop at mid section of contraction?  When Q = 100 cfs.

Solution:

E = y + V²/2g

E = y + Q²/2gA²

E = 5 + 100² /2 × 32.2 × 10² × 5²

E = 5.06’

---

Now

Y_c =2E/3

Y_c = 3.37’

---

And, E= Y_c + Q²/2gA²

     5.06 = 3.37 + 100² /2 × 32.2 × b_c² × 3.37²

     B_c  =  2.84’

---

Slope;

Before Mid Section

S₁ = (10-2.84)/25 = 0.286

After Mid Section

S₂ = (8-2.84)/25 = 0.206

  Table: Flow Surface Profile

Length (L)	Breadth	Depth (y)
( Ft )	( Ft )	( Ft )	( Ft )
0	10	5	0.589
5	8.57	4.974	0.696
10	7.14	4.934	0.851
15	5.71	4.858	1.096
20	4.28	4.672	1.555
25	2.85	3.494	3.249
30	3.88	4.565	1.77
35	4.91	4.778	1.31
40	5.94	4.875	1.047
45	6.97	4.928	0.873
50	8	4.96	0.75

 Flow Surface Profile: