When I wrote about korat ruach קורת רוח, I sort of assumed that the synonymous phrase nachat ruach נחת רוח (literally "resting/quietness of the spirit", but also meaning satisfaction or pleasure, was of a similar construct. So I thought that the first word of the phrase - nachat - was detached from the construct phrase. But I was mistaken - the word appears on its own a few times in the Bible (Kohelet 4:6, 6:5, 9:17; Yeshaya 30:15; Mishlei 29:9). There are of course plenty of other nouns ending in the letter tav that aren't part of a construct phrase - tzalachat צלחת - "plate" and mitpachat מטפחת - "kerchief", to name two. And Klein points out that nachat comes from the root נוח - "to rest", just as shachat שחת "pit, grave" - comes from the root שוח - "to bow down, bend".
As you might imagine, the Yiddish word nachas (or naches) is closely related to the Hebrew nachat. In Yiddish it has taken on a slightly more specific meaning - often referring to the joy parents get from seeing their children's accomplishments. (As a kid in Jewish day schools, my friends and I would often have fun looking at the school yearbooks, and reading the dedications that parents wrote. We would substitute the word nachas with "nachos", leading to ridiculous phrases such as "You are a great source of nachos for your family...")
In this 2005 column, Philologos makes an interesting connection between the early use of the phrase in Kohelet 4:6 and the Yiddish expression "shep nachas". He writes (I've added the Hebrew text in brackets):
Where does the expression shepn nakhes actually come from? As often turns out to be the case with Yiddish expressions, the answer probably lies in the Bible. Yiddish nakhes comes from Hebrew nahat [נחת], “tranquility” or “contentment,” words with only a few biblical occurrences. One of these is in the verse in Ecclesiastes, Tov m’lo khaf nah.at mim’lo h.ofnayim amal u’re’ut ru’ah. [טוֹב מְלֹא כַף נָחַת מִמְּלֹא חָפְנַיִם עָמָל וּרְעוּת רוּחַ], “Better a handful of tranquility [nah.at] than two hands full of toil and vexation” — or, to paraphrase it in contemporary English, “Better to relax and enjoy life than always to strive and be frustrated.”
The image of a “handful” and “two hands full” on which this verse is based suggests the act of reaching into something — a sack of wheat, a pot of food, a bucket of water or whatever — and scooping up, or trying to scoop up, its contents. It’s wiser, the Bible tells us, to scoop up less and get pleasure from it than to scoop up more and have to struggle to keep it.
The Yiddish shepn, means, and is cognate with, the English "scoop" (note the very similar Dutch scheppen).