By simple observation, even in the fast flowing bits if you throw a tennis ball in you can usually keep pace with it walking (6km /hour) and a tennis ball is a fair indicator as you can see it, but it is also fairly close to neutral buoyancy so it behaves like the water. However, there is actually a lot more slow moving water than fast moving, not by distance necessarily but certainly by rate of flow, such as Holne Weir where 10m / minute (600m /hour) is about it. Leaves or feathers that float on the surface are no good because they are adversely affected by eddies and breezes so that even a light breeze will blow a leaf upstream against the flow.
Now it is 28km from Dartmeet to Totnes Weir and say that 1/2 (14000m) is flowing at the 6000m/hour rate and the rest at 600m/hour.
So 14000m / 6000m/hour = 2.33hours
14000m / 600m/hour = 23.3 hours
In other words it takes the water 1 day to get from Dartmeet to Totnes Weir.
However, I think that the slow flow rate is still too fast given the differential in the time it takes me to swim 1/2 mile downstream to Totnes Weir vs the time to swim back against the current which would give the flow in that section as 6-7m /min and in total accounts for 10% of the distance as the same conditions prevail for 1 mile upstream of the weir. And the fast rate is too fast given that it is determined against walking pace and 6km/hour would be a reasonable pace along clear, level tow path and none of the path down the river is like that. (I know it looks faster but the water in the rapids does not go in a straight line but jumps about all over the place.)
(By now you should have begun to realize I have spent far too much time thinking about this, time to call the people in white coats.)
There is of course another factor which is that in some places the water eddies quite magnificently such as at Sharrah Pool where there are 2. Now if a drop of water moved in a direct line from Dartmeet to Totnes then maybe it would make the journey in 24 hours. But the water drop could be caught in all the counter eddies which might add significantly to the journey time. The problem here is determining what % of the flow gets caught and for how long which would serve to increase the average time taken for any randomly chosen drop of water.
Furthermore this considers only the water at the surface mid-channel clear of the banks, whereas water in the depths or where it meets obstructions at the bank will be slowed.
Consequently 24 hours from Dartmeet to Totnes under typical water levels is probably a minimum figure. It would not surprise me if the actual time for a single drop of water is actually twice that: 48 hours. In flood conditions the time would be a lot less of course and I have heard an average flow of 4mph mentioned by canoeists based on the time taken to cover the loop from New Bridge to Holne Bridge (2 miles) which would cover Dartmeet to Totnes in 4.5 hours.
Far, far too much time spent on this.
But that is not source to sea. Upstream of Dartmeet there is another 17km on the East Dart to source, we’ll use that (but 20km on the West Dart) and from Totnes Weir it is 18km to Dartmouth Castle and the open sea.
The flow above Dartmeet is if anything more uniform as the river itself is more uniform and even the pools have a flow. For the sake of argument call it 1000m / hour (because I can easily out walk the tennis ball floating in the river) and that adds another 17 hours.
That leaves the estuary where flow is undeniably seaward but not all the time! In thinking about this before I swam the OSS Dart 10k event I concluded that on an outgoing tide the flow is about 600m/ hour. But every 6 hours the water flows the wrong way, but how much? That is a complete guess and consequently no help. On the other hand if water is arriving down the river at the weir at a rate of 600m/hour then on average it must be leaving the weir at a minimum of 600m/ hour otherwise if flow in was greater than flow out there would soon be a very big puddle. 600m/hour is of course exactly what I calculated the outflow of the tide to be, it cannot be coincidental.
So source to Dartmeet = 17 hours, Dartmeet to Totnes = 24 hours and now Totnes to sea = 30 hours.
Shall we round up, call it 72 hours or 3 days from source to sea.
With a margin of error of about a week.
And with that it is time to towel off and get dry.