In 推移 there are two distinct sounds, like "suy ee". In some languages the first い would be unambiguously rendered (transcribed) as a consonant, while the second as a vowel. This is not the case with ふうう.

@macraf I'm not sure to understand what does it mean to render "i" as a consonant and in which languages does that occur. And anyway, aren't we just talking of Japanese here and Japanese pronunciation? I mentioned 推移 just because is an example of word that might have a tricky pronunciation due to two consecutive vowels.

Because there are two different sounds, what you wrote (an example of 推移 as ending with two vowels) is not actually true. These are not two vowels; the first part - すい is not "su ee", it is akin to "suy" which you can't extend to 30 seconds when uttering (if it indeed ended with a vowel, you would be able to). Japanese writing system (which does not have a concept of vowels and consonants anyway) uses い for both; other transcriptions are less ambiguous. It is clear even in English as I mentioned in my previous comment. "-y" is different from "ee-".

@macraf whether what you say is true or not, I just meant to provide a simple answer to help the OP understand how to pronounce a certain word. That's it. 推移 is not even relevant to the answer itself, it was just an instance of a word that might be difficult to pronounce for a reason that, if not the same as you point out, we can agree is at least close enough. Then if you wanna keep splitting hairs that's another story.

You wrote "this isn't the only example of words ending with two vowels in Japanese. For example, 推移" and I'm commenting on that. It's not true that this word has two consecutive vowels. StackExchange provides a commenting function and I'm using it to point out a mistake. There is no rule that comments should be limited to those parts which you think are relevant and forbidden for those parts you consider "not even relevant".

【前半】北部九州では「[酔]{す} い sour」、「[濃]{こ} い dense」を「すいー」、「こいー」と母音を伸ばして発音します。TommyはＯＰが提示した「風雨」の発音は「フウー」では‌​ない、「フウう」であることを分かりや‌​すく‌​伝えるために「推移」を例に持ってきたこと‌​は明らかです。例としては「水位」でも同じ‌​でしょう。これらは「スイー」ではなく、「‌​スイい」と発音します。‌​確かに「推移」「水‌​位」の例で最初の「イ」を３０秒間伸ばすの‌​は難しいと思いますが、北部九州の人は「ス‌​イーい」と簡単に発音できると思います。そ‌​れどころ‌​か「スイーツ sweet」の発音では日本人なら誰でも「イ」を３０秒間伸ばせます。その理由は「推移」「水位」における「推」「水」の発音で‌​は、「スイ」の「ス」にアクセントがあ‌​るか‌​らです。

【後半】北部九州の「酔いー」「濃いー」においては「イ」にアクセントがあります。アクセントのある位置で一般に息を多く吐き出‌​しますので、アクセント位置以外では音‌​を伸‌​ばすのが難しいのです。つまり、アクセント‌​位置によって母音が伸ばしやすいかどうかが‌​決まります。ですから、「推移（スイい）」‌​の「イ」が３０秒間伸ば‌​せないから母音では‌​ないとは言えません。最後にTommyの提‌​示した「推移」は「風雨」の発音を理解する‌​上で良い例だと思います。また、macra‌​fさんは‌​今回の件に関して日本語の母音の発‌​音などに関するご自身の質問を提示すること‌​をお勧めします。

@mackygoo It's not really different from и and й in Russian, or "I" and "j" in German. You claim it's a good example, I claim it's false and misleading. We have different opinions. すいい could have been an analogous example to ふうう, if the first part (ふう) was pronounced like "foow" ("фул" in Russian or "fuł" in Polish), but it's not.

@mackygoo ありがとう！

@macraf You're wrong. い in Japanese is a vowel - Japanese speakers can extend いs about as long as their あs, うs, えs, and おs: until their breaths run out. Whether or not a "y" sound is considered a consonant in another language has no bearing whatsoever on Japanese.SE.

@snailplane But what is a vowel? Did I claim something was not a vowel? Do you mind actually pointing out to what you refer to? I claimed there is a consonant in-between.

@Will I'm not sure what you wanted to say. Any human being can extend a vowel as long as the breath flow permits. Japanese are no different, what you admitted (but why did you feel a need to?). You also pointed out to a new topic, that "y" in English can stand for a vowel as well as a consonant. Nice feature. Now please tell me why い in Japanese would be devoid of that a feature?

@macraf You're the one claiming that すいい is not analagous to ふうう in spite of several native Japanese speakers explaining to you that they behave exactly the same when it comes to lengthening. Hence, the burden of proof lies on you.

@Will Thank you for responding politely to my question. Impressive answer.