# Manual Calculation

a) Calculation

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

$Culvert=&space;1&space;nos$

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

b) Inlet Checking

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

$A=\frac{\pi&space;D^{2}}{4}=\frac{\pi&space;(0.6)^{2})}{4}=0.283&space;m^{2}(3.0433&space;ft^{2})$

$\frac{Q}{AD^{0.5}}=\frac{31.7820}{(3.0433&space;x&space;1.9685^{0.5})}=7.443&space;>&space;4(submerged)$

c= 0.0398, Y= 0.67

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

$\left&space;[&space;\frac{HW_{i}}{D}&space;\right&space;]=0.0398\left&space;[&space;7.443&space;\right&space;]^{2}+0.67-0.5\left&space;(&space;0.008&space;\right&space;)$

$\left&space;[&space;\frac{HW_{i}}{D}&space;\right&space;]=2.872$

$HW_{i}=1.723&space;m$

c) Outlet Control Headwater Depth at Inlet

$Critical&space;depth,&space;dc=&space;0.571m$

$\frac{dc&space;+D}{2}=\frac{0.571+0.6}{2}=0.586$

$Tailwater,&space;TW=36.59-35.09=1.5m$

$so,&space;h_{o}=TW=1.5m$

d) Determine H

$K_{e}=0.5$

$n=0.012$

$A=&space;0.283&space;m^{2}$

$V=&space;\frac{0.9}{0.283}=3.183&space;m/s$

$P=&space;\pi&space;D=\pi&space;(0.6)=1.885m$

$L=25m$

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

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

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

$H=1.232m=&space;\left&space;(&space;1+0.5.\frac{2(9.81)(0.012)^{2}(25)}{\frac{0.283}{1.885}^{4/3}}&space;\right&space;)\frac{3.183^{2}}{2(9.81)}$

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

$HW_{o}=1.232&space;+&space;1.5-0.0084(25))$

$HW_{o}=2.522&space;m$

$HW_{i}>&space;HW_{o}=1.723&space;<&space;2.522&space;(Outlet&space;Control)$

f) Outlet Velocity

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

Velocity at Outlet Vo= (0.9/0.283)=3.183 m/s

Velocity at downstream V= (0.9/1.767)=0.509 m/s

Vo/V= 6.250
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