Коль скоро заявку на ремонт приняли, перепад давления запишут.

Here коль скоро means since, seeing that, or now that.

In this sentence, it introduces the reason/background for the main action:

• Коль скоро заявку на ремонт приняли, ...
• Since the repair request was accepted, ...

A few notes:

• It sounds bookish, formal, or a bit old-fashioned in everyday speech.
• In modern conversational Russian, people would more often say:
  • раз
  • поскольку
  • раз уж

So a more neutral version might be:

• Раз заявку на ремонт приняли, перепад давления запишут.

Because коль скоро introduces a subordinate clause.

The first part:

• Коль скоро заявку на ремонт приняли

is the dependent clause, and the second part:

• перепад давления запишут

is the main clause.

Russian normally separates this kind of clause with a comma, just as English often does with since, because, or now that clauses.

Заявку is the accusative singular of заявка.

Base form:

• заявка = request / application

In the sentence, it is the direct object of приняли:

• приняли что? → заявку
• accepted what? → the request

So:

• заявка → nominative
• заявку → accusative

This is a very common feminine noun pattern:

• книга → книгу
• машина → машину
• заявка → заявку

Заявка на ремонт means a repair request or more literally a request for repair.

The phrase на ремонт is attached to заявка and shows what the request is for.

• заявка = request
• на ремонт = for repair

This structure is very common in Russian:

• билет на поезд = ticket for the train
• деньги на еду = money for food
• заявка на ремонт = request for repair

Also note:

• ремонт is after на
• here it looks the same as the dictionary form because ремонт is masculine inanimate, and its accusative singular matches the nominative singular

This is a very common Russian pattern: 3rd person plural with no stated subject.

• приняли literally means they accepted
• but Russian often uses this with an indefinite subject, where English might say:
  • they accepted it
  • it was accepted
  • someone accepted it

So заявку на ремонт приняли means something like:

• they accepted the repair request
• or, more naturally in English, the repair request was accepted

This is not unusual at all. Russian often prefers this structure when the exact people are unimportant.

Because the sentence describes a sequence:

1. first, the repair request was accepted
2. then, the pressure differential will be recorded

So:

• приняли = past
• запишут = future

This makes logical sense: the acceptance has already happened, and the recording comes afterward.

There is also an aspect point here:

• приняли is perfective past from принять
• запишут is perfective future from записать

Perfective verbs fit well here because both actions are viewed as completed events.

Перепад давления is the direct object of запишут, so yes, it is in the accusative.

But the form does not change because:

• перепад is a masculine inanimate singular noun
• for masculine inanimate nouns, nominative = accusative

So:

• nominative: перепад
• accusative: перепад

That is why it looks unchanged.

The second word, давления, is in the genitive because it depends on перепад:

• перепад чего? → давления
• a difference / fluctuation of what? → of pressure

It usually means a pressure difference, pressure differential, pressure drop, or pressure fluctuation, depending on context.

Literally:

• перепад = difference, drop, change, fluctuation
• давления = of pressure

So the full phrase is a technical or semi-technical expression.

The best English translation depends on the field:

• in engineering: pressure differential
• in maintenance/technical contexts: pressure drop or pressure fluctuation

For the same reason as приняли: Russian is using an indefinite-personal construction.

• запишут literally = they will record/write down
• but the sentence does not care exactly who they are

English often handles this by using:

• they will record it
• it will be recorded

So перепад давления запишут can be understood as:

• they will record the pressure differential
• or the pressure differential will be recorded

Yes. The most marked part is коль скоро, which sounds literary or formal. A more everyday version would be:

• Раз заявку на ремонт приняли, перепад давления запишут.
• Поскольку заявку на ремонт приняли, перепад давления запишут.

You could also make it more explicitly passive:

• Раз заявка на ремонт принята, перепад давления запишут.
• Раз заявку на ремонт приняли, перепад давления зафиксируют.

Depending on context, зафиксируют may even sound more natural than запишут if the idea is officially recording/logging a reading.

Usually in a sentence like this, коль скоро is understood as since / seeing that / given that, not as soon as.

A native speaker is likely to read it as a causal connection:

• Since the repair request was accepted, they will record the pressure differential.

If you clearly wanted as soon as, Russian would more naturally use:

• как только
• сразу как

For example:

• Как только примут заявку на ремонт, запишут перепад давления.

So in your sentence, коль скоро is better understood as since / now that.