# Manual Calculation

a) Calculation

$Flow,&space;Q=0.9&space;m^{3}/s&space;(31.7820&space;ft^{3}/s)$

$Culvert=&space;1nos$

$Q/per&space;culvert&space;=&space;0.9&space;m^{3}/s&space;(31.7820&space;ft^{3}/s)$

b) Inlet Checking

$B=0.75m&space;(2.4606&space;ft)$

$D=0.6&space;m&space;(1.9685&space;ft)$

$A=B&space;x&space;D&space;=0.75&space;x&space;0.6=0.45&space;m^{2}(4.8436&space;ft^{2})$

$\frac{Q}{AD^{0.5}}=\frac{31.7820}{(4.8436&space;x&space;1.9685^{0.5})}=4.677>&space;4&space;(Submerged)$

c=0.0347, Y=0.81

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

$\left&space;[&space;\frac{HW_{i}}{D}&space;\right&space;]=0.0347\left&space;[&space;4.677&space;\right&space;]^{2}+0.81-0.5\left&space;(&space;0.008&space;\right&space;)$

$\left&space;[&space;\frac{HW_{i}}{D}&space;\right&space;]=1.565$

$HW_{i}=0.939m$

c) Outlet Control Headwater Depth at Inlet

Critical depth,

$dc=0.467\left&space;(&space;\frac{Q}{NB}&space;\right&space;)^{2/3}$

$dc=0.467\left&space;(&space;\frac{0.9}{(1x0.75)}&space;\right&space;)^{2/3}=0.528$

$\frac{dc+D}{2}=\frac{0.528+0.6}{2}=0.528m$

$Tailwater,&space;TW=36.59-35.09=1.50m$

$so,&space;h_{o}=TW=1.50m$

d) Determine H

$K_{e}=0.5$

$n=0.012$

$A=0.450&space;m^{2}$

$V=\frac{0.9}{0.450}=2.00&space;m/s$

$L=&space;25m$

$g=9.81&space;m/s^{2}$

$S=\frac{35.30-35.09}{25}=0.0084$

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

$H=0.462m&space;=\left&space;(&space;1+0.5\frac{2(9.81)(0.012)^{2}(25)}{\frac{0.450}{2.7}^{4/3}}&space;\right&space;)\frac{2.00^{2}}{2(9.81)}$

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

$HW_{o}=0.462+1.5-0.0084(25)$

$HW_{o}=1.752&space;m$

$HW_{i}>&space;HW_{o}=0.939&space;<&space;1.752&space;(Outlet&space;Control)$

f) Outlet Velocity

$Q=&space;AV,&space;V=\frac{Q}{A}$

Velocity at Outlet Vo= (0.9/0.45)=2.00 m/s

Velocity at Downstream V =(0.9/1.125)=0.8 m/s

Vo/V= 2.5

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