🧩 The Physics Puzzle
Two identical tanks start with the same water level. Tank X: A person stands still on the piston. Tank Y: A person jumps up and down. The average force from both is exactly the same. Question: Which tank empties first?
Tank X
Level: 2.00m
Flow: 0.00 L/s
→
0.00m ahead
(0% faster)
(0% faster)
←
Tank Y
Level: 2.00m
Flow: 0.00 L/s
⚙️ Simulation Controls
📊 Water Level Over Time
📈 Live Analysis
Tank X Avg Flow
0.000 m³/s
Tank Y Avg Flow
0.000 m³/s
Why? Flow ∝ √Pressure. Since √x is concave, Average(√P)
< √(Average P). This is Jensen's Inequality!
The Solution
🏆 Tank X (Static) Always Wins!
The Explanation
Flow velocity follows Torricelli's Law:
Velocity ∝ √(Pressure)
Tank X has constant pressure. Tank Y fluctuates but has the same average pressure.
The square root function is CONCAVE (curves downward).
Jensen's Inequality states:
Average(√P) ≤ √(Average P)
Tank Y's average flow is always lower. The static load wins!