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(One) feels disappointed or disheartened. My heart sank when I saw that the meal I'd spent all day preparing had burned in the oven.
sink so low
To lower one's ethical standards (or perceived standards) by behaving in a malignant, self-centered, or despicable manner. In the wake of these vicious attacks, it's horrible to think that our fellow citizens could sink so low in the name of patriotism. I knew John wasn't the most philanthropic guy around, but I never expected him to sink so low.
sink (one's) differences
Of multiple people or groups of people, to forget about or put aside the things that one argues about, disagrees with, or dislikes about the other side, usually in order to achieve a common goal. It's really remarkable to see the two factions sink their differences in the name of reclaiming their country as a sovereign state. We'll need to sink our differences if we hope to establish peace in the region.
(one's) heart sinks into (one's) boots
One becomes suddenly disappointed, disheartened, or despondent due to an undesirable outcome or turn of events. His heart sank into his boots when he realized that she wasn't going to accept his marriage proposal. It's horrible having to deny people entry visas and watch their hearts sink into their boots, but it's just a part of the job.