Manual Calculation

a) Calculation

Flow

$Q=4.8m^{3}/s (169.5042 ft^{3}/s)$

$culvert=2 nos$

$Q/per culvert= 2.4 m^{3}/s (84.7521 ft^{3}/s)$

b) Inlet Checking

D= 1.05m (3.445 ft)

$A=\frac{\pi D^{2}}{4}=\frac{\pi (1.05)^{2})}{4}=0.8659 m^{2}(9.320 ft^{2})$

$\frac{Q}{AD^{0.5}}=\frac{84.7521}{9.320x3.445^{0.5}}=4.899> 4(submerged)$

C=0.0398, Y=0.67

$\left [ \frac{HW_{i}}{D} \right ]=c\left [ \frac{Q}{AD^{0.5}} \right ]^{2}+Y+Z$

$\left ( \frac{Hw_{i}}{D} \right )=0.0398(4.899)^{2}+0.67-0.5(0.013)$

$\left [ \frac{HW_{i}}{D} \right ]=1.619$

$HW_{i}=1.70 m$

c) Outlet Control Headwater Depth at Inlet

Critical depth $dc=0.876 m$

$\frac{dc+D}{2}=\frac{0.876+1.05}{2}=0.963m$

$Tailwater, TW=58.3-57.5=0.8m$

$so, h_{o}=\frac{dc+D}{2}=\frac{0.876+1.05}{2}=0.963m$

d) Determine H
$K_{e}=0.5$

$A=0.866 m^{2}$

$V= \frac{2.4}{0.866}=2.772 m/s$

$P=\pi d=\pi (1.05)=3.299m$

$g=9.81 m/s^{2}$

$s=\frac{57.98-57.50}{36}=0.01333$

$H=\left ( 1+k_{e}\frac{2g.n^{2}.L)}{\left ( R \right )^{4/3}} \right ).\frac{v^{2}}{2g}$ (Eq 7.5)

$H=0.824\left ( 1+0.5\frac{2(9.81)(0.012)^{2}(36))}{\left ( \frac{0.866}{3.299} \right )^{4/3}} \right ).\frac{2.772^{2}}{2(9.81)}$

$HW_{o}=H+h_{o}-SL$ (Eq 7.6)

$HW_{o}=0.824+0.963-(0.01333(36)$

$HW_{o}=1.307 m$

e) Check Headwater Control
$HW_{i}> HW_{o}=1.700> 1.307 (Inlet Control)$

f) Outlet Velocity

If given $dn=0.489, \theta =172.14^{o}$

$P=\frac{172.14 x 1.05}{2}=0.789 m (2.5886 ft)$

$A(wet)=\frac{1.05^{2}}{8}(172.14-sin 172.14)$

$=0.395 m^{2}(4.2516 ft^{2})$

$R=\frac{4.2516}{2.5886}=1.6424$

$Q=1.49 \frac{4.2516}{0.012}.1.6424^{2/3}.0.013^{1/2}$

$Q= 84.7521 ft^{3}/s$

If, TW =0.8m

$\theta =243.2^{o}$

$A(wet)=\frac{1.05^{2}}{8}(243.2-sin 243.2)$

$A(wet)= 0.708m^{2}$

Velocity at Outlet Vo= (2.4/0.395)=6.076 m/s

Velocity at downstream V=(2.4/0.708)=3.3898 m/s

Vo/V=1.792

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