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I have created a Channel Network polyline shapefile from the Channel Network tool in QGIS.

I now need to select any channel routes which flow through the red polygon as shown below.

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The attribute table for the Channel Network is shown below. I have added the unique reference (e.g 436 in this case) by buffering all the Channel Network features, merging all the buffers, assigning each buffer a unique ID then applying the unique reference to each part of the Channel Network.

enter image description here

If I merge all the Channel Network together based on the unique ID then select the Channel Networks which intersect the red polygon the selection includes Channels which do not flow through. The screenshot below shows a simplified example:

enter image description here

How can I only select the routes which flow through the red boundary from their start to finish and ignore any other channels?

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