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It may just be in a few cases, but in the case of a flute, a higher pitch appears to come with a perceived higher volume. Is this simply because you need to put more energy into the flute to get a higher harmonic? Why is that? It seems that one shouldn't need to put in more energy, and get a consequently a higher volume.

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I'm not sure how you control dynamism for a flute, but consider a piano: if you play higher pitch keys with the same strength as lower pitch keys, the higher pitch keys sound softer. –  sujeet Jun 10 '13 at 2:23
    
It is explained here that the embouchure riser acts as a resonator of high frequencies. Hence the stronger sound intensity at those frequencies. –  fffred Jun 10 '13 at 4:20

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The physiology of human ear (and perhaps brain) makes sounds with frequency ~3000 Hz sound louder than higher and lower frequencies, for same sound wave pressure perturbation; see https://en.wikipedia.org/wiki/Equal-loudness_contour

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