soup, juice, broth, sap, gravy, pus
汁 centers on liquid extracted or released from something: soup, juice, broth, sap, gravy, and even bodily fluid like pus. The common thread is a flavorful or meaningful liquid that comes from a source.
汁 combines 氵 (water) with 十, which likely acts as a phonetic component. The character expresses liquid, especially flavorful or extracted liquid.
Water 氵 plus ten 十: imagine ten different liquids—soup, juice, broth, sap, gravy, pus—all flowing together. 汁 is the catch-all for extracted liquids.
For ジュウ, picture ten (十, じゅう) bowls of soup lined up: 十 -> ジュウ, and each bowl is filled with 汁.
juice; sap
lye
miso soup
fruit juice
pork miso soup; miso soup with pork and vegetables
meat soup; bouillon; juices (from grilled meat); gravy
shiruko; sweet red-bean soup with mochi
soup
bile; gall
broth
India ink; China ink
bittern; concentrated solution of salts (esp. magnesium chloride) left over after the crystallization of seawater or brine
broth; stock; sauce
milk (of a mammal)
one-plate meal; simple meal; austerity diet
(liquid) nasal mucus; nasal discharge; pituita; snot
bitter liquid; bitter experience
soup made from boiling leftover fish scraps; fishhead soup
the lion's share; the cream
to be onto a good thing; to make money without working; to line one's pockets