Jeg tørrer vandet op med en karklud, mens hun holder øje med røret under vasken.

In Danish, the definite article is usually attached to the end of the noun.

• vand = water
• vandet = the water
• rør = pipe
• røret = the pipe
• vask = sink
• vasken = the sink

So instead of putting a separate word before the noun, Danish often adds a suffix:

• common gender: -en
• neuter: -et

A separate word for the appears mainly when there is an adjective:

• vandet = the water
• det kolde vand = the cold water

Because it refers to specific water, not water in general.

Here, the speaker is wiping up some particular water that is already there, so Danish naturally uses the definite form vandet = the water.

Compare:

• Vand er vigtigt. = Water is important.
• Jeg tørrer vandet op. = I’m wiping up the water.

English sometimes uses bare nouns more freely than Danish, but in a situation like this, vandet is the normal choice.

At tørre op means to wipe up or to dry up in the sense of removing spilled liquid.

So:

• Jeg tørrer vandet op = I’m wiping up the water

Without op, at tørre often just means to dry or to wipe more generally.

Compare:

• Jeg tørrer bordet. = I wipe/dry the table.
• Jeg tørrer vandet op. = I wipe up the water.

The op adds the idea of cleaning up something, especially a spill or mess.

Because at tørre op is a separable verb expression.

In Danish main clauses, the finite verb comes early, and particles like op are often placed later in the clause:

• infinitive: at tørre op
• present tense main clause: Jeg tørrer vandet op

This is similar to English separable phrasal verbs:

• wipe up the water
• wipe the water up

So tørrer and op belong together in meaning, even though they are separated in the sentence.

That is the normal placement here.

The core structure is:

• Jeg tørrer vandet op
• then an extra phrase: med en karklud

So the sentence is built like this:

• subject: Jeg
• verb: tørrer
• object: vandet
• particle: op
• adverbial/instrument: med en karklud

The phrase med en karklud tells you how the action is done, so it comes after the main verb phrase.

Karklud means dishcloth, dish rag, or cleaning cloth, depending on context.

It is a common-gender noun in Danish, so its indefinite singular form takes en:

• en karklud = a dishcloth

Its definite form is:

• karkluden = the dishcloth

This is just something you have to learn with each noun in Danish: whether it is an en-word or an et-word.

Mens means while and introduces a subordinate clause.

So:

• Jeg tørrer vandet op med en karklud = main clause
• mens hun holder øje med røret under vasken = subordinate clause

It shows that the two actions happen at the same time:

• I wipe up the water
• while she keeps an eye on the pipe under the sink

At holde øje med is an idiomatic expression meaning:

• to keep an eye on
• to watch
• to keep track of

So:

• hun holder øje med røret = she is keeping an eye on the pipe

This is a very common Danish expression, and it should be learned as a whole chunk, not word by word.

Because at holde øje med noget/nogen is the fixed pattern.

You holde øje med something or someone.

Examples:

• Jeg holder øje med børnene. = I’m keeping an eye on the children.
• Hun holder øje med røret. = She’s keeping an eye on the pipe.

Even though English also uses with in some expressions, here the Danish med is just part of the idiom and should be memorized together with holde øje.

The main noun is røret = the pipe.

Then under vasken adds more information about which pipe:

• røret under vasken = the pipe under the sink

So under vasken functions like a modifying prepositional phrase.

Also note:

• under = under
• vasken = the sink

Because it is a specific sink, Danish uses the definite form vasken.

Yes.

In the main clause, Danish follows the usual V2 pattern, where the finite verb comes in second position:

• Jeg | tørrer | vandet op med en karklud

In the mens clause, the conjunction introduces a subordinate clause, and the word order is the normal subordinate-clause order:

• mens hun holder øje med røret under vasken

A useful comparison:

• Jeg tørrer vandet op, mens hun holder øje med røret.
• Mens hun holder øje med røret, tørrer jeg vandet op.

In the second version, because the subordinate clause comes first, the main clause shows inversion:

• tørrer jeg instead of jeg tørrer

So yes, the word order in your sentence is completely natural.