Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce drank as DRANGK (/dræŋk/). In "drank", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, a hallmark of natural-sounding American speech. It comes out as DRANGK. You'll hear it in sentences like "I drank a lot of water today" or "He watched an old film and drank cold milk to relax" — more examples below.
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1 syllable, 5 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Before NG, the vowel changes to sound more like the AY (/eɪ/) diphthong. The middle part of the tongue lifts toward the roof of the mouth, then the front part arches up.

Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

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The textbook way isn't wrong — it's just not how anyone actually says it.
In "drank", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".
In "drank", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. Vowel changes to sound like /eɪ/ ("ay" as in "say").