Pod pretpostavkom da je interval između davanja krvi dovoljan, potpisaće obrazac.

It is a fixed expression meaning assuming that, on the assumption that, or provided that.

So Pod pretpostavkom da je... introduces a condition or assumption before the main action.

It is more formal than plain ako (if). In administrative, medical, or official language, this kind of phrasing is very common.

Because the preposition pod here requires the instrumental case.

• nominative: pretpostavka
• instrumental singular: pretpostavkom

So pod pretpostavkom literally means something like under the assumption.

This is one of those combinations you mainly learn as a set phrase:

• pod uslovom da = provided that
• pod pretpostavkom da = assuming that

Da je is perfectly natural here. It presents the condition as an assumed state:

• pod pretpostavkom da je interval dovoljan
  = assuming that the interval is sufficient

Using da bude is also possible in some contexts, but it usually sounds a bit more prospective or dependent on what turns out to be the case.

Very roughly:

• da je = assuming it is
• da bude = assuming it will be / turns out to be

In this sentence, da je is the normal, neutral choice.

The preposition između means between and it takes the genitive case.

That is why the noun after it is not in nominative form.

Here, davanje is a verbal noun meaning giving or donation. After između, it appears as davanja.

So:

• između davanja krvi = between blood donations / between acts of giving blood

A useful thing to know is that this kind of verbal noun is very common in formal Serbian.

Formally, davanja can be ambiguous, because that shape can correspond to more than one grammatical interpretation. But in this sentence, the phrase is understood naturally as referring to blood donation events in general.

So the meaning is:

• interval između davanja krvi
  = the interval between blood donations

In practice, that is how a learner should understand it.

Because davanje krvi is a verbal-noun construction, and the thing being given is commonly expressed in the genitive.

Compare the logic of English the giving of blood.

Here:

• krv = blood
• krvi = genitive singular of krv

So:

• davanje krvi = giving blood / blood donation

This pattern is very common in Serbian:

• čitanje knjige = reading a book
• pisanje pisma = writing a letter
• davanje krvi = donating blood

Because adjectives in Serbian must agree with the noun they describe.

The noun here is interval, which is:

• masculine
• singular

So the adjective must also be masculine singular:

• dovoljan interval = a sufficient interval
• interval je dovoljan = the interval is sufficient

That is why you get dovoljan.

Because Serbian often drops subject pronouns when the subject is understood from context. This is called a pro-drop language.

So instead of saying:

• On/ona će potpisati obrazac

Serbian can simply say:

• Potpisaće obrazac

The verb form tells you it is third person, and the surrounding context tells you who that person is.

This is very normal in Serbian.

Potpisaće is the future tense of potpisati (to sign).

It is the contracted written form of:

• će potpisati

In standard Serbian spelling, future forms are often written as one word by attaching the future clitic to the infinitive stem:

• potpisati → potpisaće

One important detail: potpisaće can mean either:

• he/she will sign
• they will sign

So by itself, it does not show gender, and in this form it also does not clearly distinguish singular from plural. Context does that.

It actually is in the accusative, but for masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: obrazac
• accusative: obrazac

That is why it looks unchanged.

Compare with a masculine animate noun, where you would usually see a difference:

• student → vidim studenta

But with an inanimate noun like obrazac, the form stays the same.

Because the sentence begins with a subordinate conditional/assumptive clause:

• Pod pretpostavkom da je interval između davanja krvi dovoljan, ...

After that introductory clause, Serbian normally uses a comma before the main clause:

• ..., potpisaće obrazac.

This works much like English punctuation in sentences such as:

• If the interval is sufficient, he/she will sign the form.

Yes, it sounds quite formal and a little administrative or medical.

That comes especially from expressions like:

• pod pretpostavkom da
• interval između davanja krvi
• potpisaće obrazac

A simpler, more everyday version might use ako instead:

• Ako je interval između davanja krvi dovoljan, potpisaće obrazac.

That said, the original sentence is perfectly natural in official or institutional language.