Water and fertilizer supply can affect the processes of assimilate production (source) and assimilate accumulation (sink), thereby causing differences in potato yield. However, little is known about the coupling effects of irrigation amount and potassium rate on potato tuber yield and its potential source-sink relationships. The objective of this study was to quantify how water and potassium supplies affected the source-sink relationships of drip-fertigated potato after tuber emergence. A two-year field experiment was conducted during the potato growing seasons of 2019 and 2020, with three irrigation levels (W1: 60% ET c , W2: 80% ET c and W3: 100% ET c , where ET c is the crop water requirements) and four potassium rates (K0: 0 kg ha -1 , K1: 135 kg ha -1 , K2: 270 kg ha -1 and K3: 405 kg ha -1 ). The results showed that compared with K0, the treatments viz ., K1, K2 and K3 increased average tuber yield by 1.3%, 17.3% and 15.5% in 2019 and 10.7%, 24.0% and 19.3% in 2020, respectively. However, compared with W3, the treatments viz ., W1 and W2 reduced the average tuber yield by 8.0% and 12.9% in 2019 and 8.9% and 14.7% in 2020, respectively. The beta sigmoid growth function well fitted the relationship of source capacity and sink capacity. The source capacity and source activity increased with the increase of potassium rate under W2 and W3 in 2019 and under W3 in 2020, while the sink capacity and sink activity first increased and then declined with the increasing potassium rate. Increasing water and potassium supply generally increased the vegetative growth and tuber growth time. The tuber growth rate first increased and then decreased with the increase of potassium rate, while it increased with the increasing irrigation amount. The sink-source ratio decreased with the increase of potassium rate, but there was no significant difference between K1 and K2, and the sink-source ratio under K3 was significantly lower than that in the other potassium treatments. It was concluded that potato was in source-sink balance under K1 and K2, but not under K3. The quantitative approach produced parameters that characterized the differences of source and sink capacity in response to various water and potassium supplies. Sufficient irrigation (W3) with moderate potassium application (K2) increased potato yield mainly by maintaining its source-sink balance. • A model approach was proposed to quantify source-sink relationships of potato under various water and potassium supplies. • The mechanism analysis of yield difference from various water and potassium supplies was conducted by source-sink balance. • Source-sink capacity was affected by different water and potassium management practices. • The sink-source ratio was not significantly different between 135 and 270 kg ha -1 , indicating the source-sink balance. • Various water and potassium application amounts influenced plant potassium absorption and tuber yield.