If There Was Any Doubt Of Labour's Anti...
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For more on marking an answer as the "Best Answer", please visit our FAQ.Assuming that the aquaduct is not blocked at both ends then the barge will displace it's weight in water throughout the entire system. This would effectively spread the weight over the whole water system and result in a microscopice rise in water level. So the barge would make a negligable difference to the actual weight on the aquaduct.
The increased water pressure local to the barge hull will act on both sides of the trough, and the base. It will dissipate with distance but there will be a local loading on the supports.
We have a famous aquaduct near us at a place called Froncysyllte near Llangollen. It can be used by pedestrians as well as narrow boats as they are called.