Posle davanja krvi uzmite osveženje i povećajte unos tečnosti.

Posle takes the genitive case.

That is why you get:

• davanje → davanja
• krv → krvi

So posle davanja krvi literally means after the giving of blood or more naturally after giving blood / after donating blood.

Here Serbian uses a verbal noun: davanje = giving.

So:

• davanje krvi = the giving of blood
• posle davanja krvi = after giving blood

This is very common in Serbian after prepositions like posle. English often uses an -ing form, while Serbian often uses a noun-like form.

Krvi is the genitive singular of krv (blood).

It appears in genitive because it depends on the verbal noun davanje:

• davanje čega? → krvi
  giving of what? → of blood

So inside the phrase davanja krvi, both words are in forms that fit the larger genitive structure.

Uzmite is the imperative form of uzeti (to take).

It is used for:

• more than one person: take!
• one person politely/formally: please take

In notices, instructions, and medical settings, Serbian often uses this form because it sounds polite and standard.

Grammatically, uzmite and povećajte can mean either:

• you all
• you in a polite/formal singular sense

In a public instruction like this, it is usually best understood as a polite instruction to the reader, not necessarily only to a group.

Both come from perfective verbs:

• uzeti → uzmite
• povećati → povećajte

Perfective imperatives are very natural when the speaker means:

• do this action
• complete this action
• follow this instruction

So here the meaning is roughly:

• take some refreshment
• increase your fluid intake

If Serbian used imperfective forms, it could sound more like an ongoing or repeated process, depending on context.

Literally, osveženje means refreshment.

In this context, it usually means something like:

• a light drink
• a snack
• refreshments offered after donating blood

So uzmite osveženje is a standard way of saying have some refreshment or take a refreshment/snack.

Literally:

• unos = intake
• tečnosti = of liquid / of fluids

So povećajte unos tečnosti means increase fluid intake.

This is a very common medical or health-style expression. It sounds a bit formal, just like English increase your fluid intake.

Here tečnost is being used as an uncountable noun, like liquid or fluid in English.

So unos tečnosti means:

• intake of fluid
• fluid intake

Even though English often says fluids, Serbian can naturally use the singular abstract noun in this kind of formal expression.

Serbian does not have articles.

So where English says:

• the blood
• a refreshment
• the fluid intake

Serbian simply uses the noun form itself:

• krvi
• osveženje
• unos tečnosti

Whether something is definite or indefinite is understood from context.

Yes. Posle and nakon both mean after and both take the genitive.

So you could also say:

• Nakon davanja krvi, uzmite osveženje i povećajte unos tečnosti.

The difference is mostly stylistic:

• posle is very common and everyday
• nakon can sound a bit more formal or written

Both are correct here.

Not completely. Serbian word order is more flexible than English word order.

This sentence starts with the time phrase:

• Posle davanja krvi = After donating blood

That is a very natural choice because it sets the context first.

You could rearrange parts of the sentence, but the given version sounds clear and normal for an instruction. In public notices and medical advice, this kind of order is very common.