Learn English – How are these Brazilian Portuguese names pronounced in English

The pronunciation of Greek letters by scientists isn't very different from the pronunciation of the Greek letters in the respective countries: American scientists pronounce them pretty much the same way the general American population does, and so on.

So your question is actually about why the English pronunciation of Greek letters, and the answer is that it is based on (but not always actually very close to) the reconstruction of the Classical Greek pronunciation by Erasmus in 1528 and by John Cheke and Thomas Smith around 1540, which were adopted in schools. This pronunciation underwent some change along with the rest of English during the Great Vowel Shift, and a re-reconstruction in the mid-19th century brought it back in line (incompletely) with Ancient Greek. The Wikipedia page on Pronunciation of Ancient Greek in teaching has more details.

For sake of completeness, here's a (very incomplete) table showing the pronunciation in American English, British English, Ancient Greek, and Modern Greek. I've rearranged the alphabet to put sort-of rhyming letters together, but all letters are there.

[Disclaimer: Many of the entries may be terribly wrong. The American and British IPA entries are based on the article English pronunciation of Greek letters, the "pseudo-phonetic spellings" are from here and here. The Classical and Modern Greek pronunciation columns I made up, partly from Swedish Wikipedia, partly from piecing together each letter's pronunciation in this table, partly from here for Modern Greek, and partly on my own — and I don't actually know IPA.]

[Edit: This table has now been edited to correct the IPA and source Classical Greek pronunciations from the English Wikipedia.]

Notes:

• The table, especially the all-important Classical Greek pronunciation column, is incomplete; I ran out of patience.
• For the rhyming letters Beta-Zeta-Eta-Theta, the American pronunciation (-ayta) is closer to Classical Greek and the British pronunciation (-eeta) closer to Modern Greek.
• For the rhyming letters Phi-Chi-Psi-Xi (but not Pi for some reason!) there seems to be a variant (-ee) pronunciation close to modern Greek that exists only(?) in science and mathematics.

I've made this community wiki so that someone can fix the errors or complete the table (including possibly myself if I regain the patience to finish this sometime!)

Words with "gui" like "guide" and "guise" don't contain the "ui" digraph: instead, they have the "gu" digraph that functions to mark "hard g" before a front vowel letter (I or E).

The word suicide doesn't contain the "ui" digraph either: it has U followed by I in hiatus. This is the usual pronunciation of "ui" before a consonant letter in words from Latin, like suicide (from latin suicida).

Further background information about the "ui" digraph

As a digraph, "ui" acts as an alternative spelling of the "long u" sound in English. The basic pronunciation of the "long u" sound is /juː/, but because of "yod-dropping", the pronunciation /uː/ is used instead after /dʒ/ or /r/, or after a consonant cluster ending in /l/. The current pronunciations of the English "long u" sound are thought to have developed from a falling diphthong pronounced something like [ɪu̯]. The diphthong [ɪu̯] had several different sources:

• various diphthongs in native English words
• words from French that had in that language the front rounded monophthong /y/
• words from French with various diphthongs, such as beauty, deuce, suit from French beawté/beuté/bewté, deux, siute/sute/seute/suite

In modern Dutch, "ui" is used as a digraph representing a front rounded diphthong typically transcribed /œy̯/. This sound developed from an earlier long monophthong, as exemplified by the Dutch word bruin from Proto-Germanic *brūnaz (English brown). If the Dutch word sluis was borrowed from French before the diphthongization of long high vowels, that would explain why it has "ui".

The various changes that occurred between diphthongs and monophthongal long vowels, between and within languages, probably contributed to the diversity of spellings of the "long u" sound in present-day English.

The words bruise, juice and cruise

The word bruise is an unusual "ui" word in that it has a Germanic origin. The "ui" here is thought to have developed irregularly or dialectally from an Old English [yː] sound, which in most words lost its rounding (e.g. Old English [myːs] became modern English mice /maɪs/ via a Middle English form /miːs/). I talk a little bit more about it in my answer to the question "Relation of RUFFLER and RUYFLER".

With cruise, as the OED mentions, it seems pretty likely that the spelling was just taken from Dutch. Although the OED entry mentions cruse as a historical alternative spelling, I don't think it says that cruse used to be the more common spelling: both spellings (as well as cruize) are marked as being used starting from the 17th century. The pronunciation with /uː/ could be related to the pronunciation of Spanish/Portuguese cruzar, or it could be based on the spelling.

I don't know of any special reason for why the spelling juice won out over spellings like juce or juse. Neither of those spellings has any particular issue with representing the sound of the word: -⁠uce and -⁠use are used in the spelling of some words that rhyme with juice, such as puce, spruce, truce, reduce, use, abuse. Your suggestion of influence from other words spelled with "ui" seems the best explanation to me. I don't know of any way Dutch could have influenced the spelling of juice, since I haven't found any Dutch words spelled with ui that are related to French jus or English juice.

I'm not sure about the history of the spelling sluice.