Significance Fluid flow plays an important role during oogenesis. From insects to mice, oocytes mature by acquiring cytoplasm from sister germ cells, yet the biological and physical mechanisms underlying this transport process remain poorly understood. To study the dynamics of “nurse cell dumping” in fruit flies, we combined direct imaging with flow-network modeling and found that the intercellular pattern and time scale of transport are in accordance with a fundamental hydraulic pressure law. Changes in actomyosin contractility are observed only in the second phase of nurse cell dumping as surface waves that drive transport to completion. These results show that tandem physical and biological mechanisms are required for complete and directional cytoplasmic transport into the egg cell.