When we try to close a water tap with our fingers, fast jets of water gush through the small opening

Question

When we try to close a water tap with our fingers, fast jets of water gush through the small openings between our fingers. Which principle best mathematically explains this observation?

Professor PC Thomas Classes · Answer

According to the equation of continuity ($Av = 	ext{constant}$), reducing the cross-sectional area (by blocking the tap with fingers) results in a proportional increase in the velocity of the fluid escaping through the remaining small gaps.