Answer:
448.8 ft
Explanation:
Area of semi-circle=[tex]0.5\times \frac {pi d^{2}}{4}=\frac {pi\times 3^{2}{4}\times 0.5=3.5325 ft^{2}[/tex]
Hydraulic radius is given by
[tex]R_h=\frac {A_c}{\pi R}[/tex] where [tex]\pi R[/tex] is wetted perimeter, [tex]A_c[/tex] is cross-sectional flow area and [tex]R_h[/tex] is hydraulic radius
[tex]R_h=\frac {3.5325}{\pi (1.5)}=0.74 ft[/tex]
From Manning’s equation, flow rate is given as
[tex]V=\frac {a A_c R_h^{2/3}S_o^{0.5}}{n}[/tex]
Here, [tex]S_o[/tex] is bottom slope, [tex]a=1.486 ft^{1/3}/s[/tex]
Manning’s coefficient is taken as n=0.014 for open unfinished concrete
Substituting 90 for v, 1.486 for a, 3.5325 for [tex]A_c[/tex], 0.74 for[tex]R_h[/tex] and 0.014 for n
[tex]90=\frac {1.486\times 3.5325\times 0.74^{2/3}\times S_o^{0.5}}{0.014}[/tex]
[tex]4.29S_o^{0.5}=1.26[/tex]
[tex]S_0^{0.5}=0.293[/tex]
[tex]S_o=0.085[/tex]
Change in elevation is given by
[tex]\triangle z=S_o L[/tex] where L is distance, here given as 1 mile
1 mile=5280 ft
[tex]\triangle z=0.085\times 5280=448.8 ft[/tex]
