Manhole Simple Loss Example: Difference between revisions
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Entry losses are applied as an exit loss on the incoming conduit and are calculated as follows:<br>
[[File:K entry.PNG]]
<br>
Where:<br>
[[File:Vp.PNG]]
<br>
With other parameters defined in the section above. The calculated flow area in the manhole is 3.6m<sup>2</sup> and 1m<sup>2</sup> in the adjacent culvert whilst the flow is 2m<sup>3</sup>/s for both Q<sub>p</sub> and Q<sub>om</sub>.
Therefore, V<sub>m</sub> equals:<br>
[[File:Vm1.PNG]]<br>
And V<sub>p</sub>:<br>
[[File:VP1.PNG]]
<br>
Using these in the K<sub>entry</sub> equation provides a loss coefficient of:<br>
[[File:K entry1.PNG]]
<br>
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===Example 1 - Exit Losses===
Exit losses are applied to the upstream end of the outgoing conduit and are calculated as follows:<br> [[File:K exit.PNG]]<br>
<br>
From table 1, we can see that K<sub>m</sub> is set to 1. A<sub>p</sub> and A’<sub>m</sub> are 1m<sup>2</sup> and 3.636m<sup>2</sup> respectively. Therefore, K<sub>exit</sub> is:<br> [[File:K exit1.PNG]]▼
<br>
▲From table 1, we can see that K<sub>m</sub> is set to 1. A<sub>p</sub> and A’<sub>m</sub> are 1m<sup>2</sup> and 3.636m<sup>2</sup> respectively. Therefore, K<sub>exit</sub> is: [[File:K exit1.PNG]]
Figure 3 shows that the calculated value matches those provided in the TUFLOW results. The value is also reported as the first value for the downstream conduit in the *_TSL_P.shp layer.
===Example 1 - Outgoing Conduit Losses===
The loss coefficient for the outgoing pipe represents the losses due to the incoming angle of the upstream conduit, any drops in inverts levels between the incoming and outgoing conduits, bend losses and any additional form losses. It is calculated as follows:<br>
[[File:K outletpipe.PNG]]<Br>
The default value of K<sub>Bend_max</sub> is set to 4 but can be changed via the 1d_mh K_Bend_Max attribute. As shown above we have no angle for the incoming pipe and no drop in invert levels. Table 1 shows the K_Fixed is equal to 2 and the outgoing pipe has a form loss coefficient, to represent bend losses of 1. Therefore K<sub>outletpipe</sub> is:<br>
[[File:K outletpipe1.PNG]]
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In this example, the flow area in the manhole is 4.12m<sup>2</sup> and 1m<sup>2</sup> in the adjacent culvert whilst the flow is 2m<sup>3</sup>/s for both Q<sub>p</sub> and Q<sub>om</sub>.
Therefore, Vm equals:<br>
[[File:Vm2.PNG]]
<br>
And V<sub>p</sub>:<br>
[[File:Vp2.PNG]]
<br>
From this:<br>
[[File:K entry2.PNG]]
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===Example 2 - Exit Losses===
In this example, A'<sub>m</sub> is 4.12m<sup>2</sup>, therefore K<sub>exit</sub>:<br>[[File:K exit2.PNG]]<br>
Which matches the result in figure 6.
===Example 2 - Outgoing Conduit Losses===
On this occasion, we have an 90 degree angle between the incoming and outgoing conduit. Therefore, we need to calculate Kθ using the following equation:<br> [[File:Ktheta.PNG]]<br>
<br>
Q<sub>f</sub> is calculated as:<br> [[File:Qf.PNG]]
<br>
Q<sub>p</sub> and Q<sub>om</sub> are both 2m<sup>3</sup>s<sup>-1</sup> and therefore Q<sub>f</sub> is equal to 1. The incoming conduit angle is 90 degrees which is cancelled out by the denominator. K<sub>θ</sub> is therefore:<br>[[File:Ktheta1.PNG]]<br>
We also have a drop between the incoming and outgoing pipes. K<sub>drop</sub> which represents losses due to this drop is calculated as follows:<br>[[File:Kdrop.PNG]]<br>
Which is:<br>[[File:Kdrop 1.PNG]]<br>
Therefore K<sub>outletpipe</sub> is:<br>[[File:K outletpipe2.PNG]]<br>
This matches the simulated value in figure 6.
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==Example 3: Multiple Incoming Conduits with Incoming Bend and Drop in Invert Levels==
In this example we have multiple incoming conduit. Each upstream conduit has a flow of 1m<sup>3</sup>s<sup>-1</sup> applied to it.<br>
[[File:Schematic 3.png|800px]]
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|'''Downstream Invert Level (m AD)''' || 99.7 || 99.8
|}
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The resulting simulated loss values are presented in Figure 8.
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===Example 3 - Entry Losses===
This time the flow area in the manhole is 3.57m<sup>2</sup> and 1m<sup>2</sup> in the adjacent culvert whilst the flow is 1m<sup>3</sup>/s for Q<sub>p</sub> and 2m<sup>3</sup>s<sup>-1</sup> for Q<sub>om</sub>. Therefore, V<sub>m</sub> equals:[[File:Vm3.PNG]]▼
<br>
▲This time the flow area in the manhole is 3.57m<sup>2</sup> and 1m<sup>2</sup> in the adjacent culvert whilst the flow is 1m<sup>3</sup>/s for Q<sub>p</sub> and 2m<sup>3</sup>s<sup>-1</sup> for Q<sub>om</sub>. Therefore, V<sub>m</sub> equals:<br>[[File:Vm3.PNG]]
And V<sub>p</sub>:[[File:Vp3.PNG]]▼
<br>
▲And V<sub>p</sub>:<br>[[File:Vp3.PNG]]
<br>
From this:<br>
[[File:K entry3.PNG]]<br>
This matches the losses for both incoming pipes as shown in figure 8.
===Example 3 - Exit Losses===
A'<sub>m</sub> is 3.57m<sup>2</sup> respectively. Therefore, K<sup>exit</sup>:<br>[[File:K exit3.PNG]]<br>
The calculated losses match the losses calculated by the TUFLOW presented in Figure 8.<br>
===Example 3 - Outgoing Conduit Losses===<br>
In this model we have two incoming pipes, one with an 90 degree angle between the incoming and outgoing conduit and one with zero.
Recall that: <br>[[File:Ktheta.PNG]]<br>
With Qf calculated as: <br>[[File:Qf.PNG]]
<br>
Q<sub>p</sub> is set to 1m<sup>3</sup>s<sup>-1</sup> and Q<sub>om</sub> to 2m<sup>3</sup>s<sup>-1</sup>. Q<sub>f</sub> is equal to 0.5m<sup>3</sup>s<sup>-1</sup>. For the incoming conduit with an angle of 90 degrees, K<sub>θ</sub> is therefore: <br>[[File:Ktheta2a.PNG]]<br>
For the incoming conduit with an angle of 0 degrees, K<sub>θ</sub> is therefore: <br>[[File:Ktheta2b.PNG]]<br>
We also have a drop between the incoming and outgoing pipes. K<sub>drop</sub> which represents losses due to this drop is calculated as follows: <br>[[File:Kdrop 2a.PNG]]
<br>
and:<br>[[File:Kdrop 2b.PNG]]<br>
Therefore, K<sub>outletpipe</sub> is: <br>[[File:K outletpipe3.PNG]]<br>
The calculated value matches that presented in figure 8 for the downstream conduit loss.
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