Three-drops water radical on the left — the side-form of 水. Sweat is the body's water, so the water radical groups 汗 with the family of bodily fluids and water-words: 泪 (tears), 汁 (juice), 涎 (saliva), 液 (liquid).
Provides the sound (gān → hàn, with shift). 干 means dry but here functions primarily as phonetic. Some learners find a memorable irony in water + dry = sweat — the body's water that ends up dried on the skin. Same phonetic in 杆 (gān, pole), 肝 (gān, liver), 竿 (gān, bamboo pole).
