## Cornelis Velsen - the experiment that he may have carried out

### NB:

The experimental write up below is not based on any historical research carried out. It is purely an hypotheses of how Cornelis Velson might have carried out any experiment of this type.

## Aim

To determine the relationship between the slope of a stream bed and the velocity of water in the stream. To define a formulae that will provide a close approximation with the actual stream velocity.

## Equipment

A fairly straight length of river or stream

Two assistants prepared to get their feet wet

A telescope on a tripod

A long pole graduated in units of length, such as metres or perhaps decimetres

Surveyors or Gunter’s chain

A pocket watch

An orange. The orange is very important.

## Description of stream survey

Cornelis would need to find the stream reach to use for the experiment. He would then need to measure the water course distance of 50.0 metres using a surveyor’s chain. The first assistant stands at the top of the measured distance in the middle of the stream channel. He has the tripod and telescope. The second assistant then stands in the stream 50.0 metres downstream of the first assistant with the graduated pole held vertically. The first assistant looks at the vertical pole through the telescope while making sure the telescope is held horizontally. He then records the graduation mark he sees in the telescope. Once the height of the graduation mark on the pole above the stream bed is known the height from the stream bed to the telescope lens is deducted to obtain the vertical drop along the channel, let’s assume it measures 2.0 metres.

Cornelis now needs the horizontal distance between the two assistants, since the 50.0 metres is the distance along the slope of the stream. In order to obtain the horizontal length, Cornelis would most likely have used Pythagoras’s theorem to find the horizontal length. This gives a horizontal distance of 49.96 metres, see note. Now, the slope of the stream channel can be calculated by dividing the vertical drop by the horizontal length. Cornelis would have found that the stream bed slope was 0.04, see note.

Cornelis now needs the horizontal distance between the two assistants, since the 50.0 metres is the distance along the slope of the stream. In order to obtain the horizontal length, Cornelis would most likely have used Pythagoras’s theorem to find the horizontal length. This gives a horizontal distance of 49.96 metres, see calculation sheet equation (2). Now, the slope of the stream channel can be calculated by dividing the vertical drop by the horizontal length. Cornelis would have found that the stream bed slope was 0.04, see calculation sheet equation (4).

Pythagoras’ Theorem:

Equation (2):

Equation (4):

## Stream Velocity

Next, he would need to find out what the actual flow velocity was. That’s when he would use the orange. With his assistants still standing in the stream channel, he would hand the orange to the assistant at the upstream location. The assistant would place the orange in the water and Cornelis would note the time on his pocket watch. As soon as the orange floated downstream and passed the second assistant, he would shout out to Cornelis, who would check his pocket watch again. Cornelis now had a distance of 50 metres that the orange had travelled downstream and how long it had taken. If we assume it took 4.0 minutes for the orange to flow along the 50 metres of the stream, then Cornelis could work out that the actual velocity of the stream was 0.208 metres per second, see note.

Next, he would need to find out what the actual flow velocity was. That’s when he would use the orange. With his assistants still standing in the stream channel, he would hand the orange to the assistant at the upstream location. The assistant would place the orange in the water and Cornelis would note the time on his pocket watch. As soon as the orange floated downstream and passed the second assistant, he would shout out to Cornelis, who would check his pocket watch again. Cornelis now had a distance of 50 metres that the orange had travelled downstream and how long it had taken. If we assume it took 4.0 minutes for the orange to flow along the 50 metres of the stream, then Cornelis could work out that the actual velocity of the stream was 0.208 metres per second, see calculation sheet equation (3).

## Results

He will now be able to work out an equation using the slope of 0.4 to get a result approximately the same as the actual velocity in the river. The square root of 0.04 is 0.200, see note which is reasonably close to the actual velocity 0.208. In actual fact, it is probable that Cornelis repeated the experiment multiple times on different rivers or different reaches of the same river before publishing his book in 1749.

He will now be able to work out an equation using the slope of 0.4 to get a result approximately the same as the actual velocity in the river. The square root of 0.04 is 0.200, see calculation sheet equation (5) which is reasonably close to the actual velocity 0.208. In actual fact, it is probable that Cornelis repeated the experiment multiple times on different rivers or different reaches of the same river before publishing his book in 1749.

Equation (5):

## Conclusion

While I have used values that show a close approximation between the experimental results and Cornelis Velsen’s equation, it was a fairly crude first attempt. Finally, I have an Empirical Formulae calculation sheet that shows the equations he may have used, see note. You can change the slope of the river and time it took for the orange to flow downstream, and you will see that his equation was a very crude approximation.

While I have used values that show a close approximation between the experimental results and Cornelis Velsen’s equation, it was a fairly crude first attempt. Finally, I have an Empirical Formulae calculation sheet that shows the equations he may have used. You can change the slope of the river and time it took for the orange to flow downstream, and you will see that his equation was a very crude approximation.

## note

The SMath Desktop Studio software shown on this website has been developed by Andrey Ivashov, a Russian.

Due to the Russian aggression against Ukraine in the Russia-Ukraine war, I have decided to break all the websites direct links with the SMath Desktop software until the war comes to an end.