Determination of flow surface profile in contraction allowing no gradual hydraulic drop in perfection

Determination of flow surface profile in contraction allowing no gradual hydraulic drop in perfection. Where Q= 100cfs,  y_u/s=5ft  and other details are given in fig below.

Solution:

As E is Constant.

E= y + V²/2g

E = y + Q²/A²2g

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So, At Upstream (u/s):

E = 5 + 100²/ (b² × y² ×2 × 32.2)

E = 5 + 100²/ (10² × 5² ×64.4 )

E=5.06’

At downstream (d/s):

E = y_d/s + Q²/ (b² × y_d/s ² × 2g)

5.06 = y_d/s + 100²/ (8² × y_d/s ² × 64.4)

y_d/s = 4.96’ &;   0 .75’

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Where; Y_c = 2/3 × E

         =2 × 5.06/3 

         = 3.37’

& Slope  = (10-8) / 50  = 0.04

Table:  Subcritical and Supercritical Depth Values For Intermediate Points
Length (L)	Breadth (b)	Depth (y)
		y1	y2
(ft)	(ft)	(ft)	(ft)
5	9.8	0.602	4.995
10	9.6	0.616	4.992
15	9.4	0.63	4.989
20	9.2	0.644	4.986
25	9	0.66	4.983
30	8.8	0.676	4.979
35	8.6	0.693	4.975
40	8.4	0.711	4.971
45	8.2	0.73	4.966
50	8	0.75	4.961