Torricelli's Law & Water Tank Drainage Calculator
Calculate liquid discharge velocity (v = Cd√2gh), drain hole flow rate in GPM, and total time to empty a cylindrical tank using Torricelli's law.
Calculated Results
Frequently Asked Questions
What is Torricelli's Law of fluid efflux?
Discovered in 1643 by Evangelista Torricelli, the law states that the exit speed of a fluid through a sharp orifice under gravity equals the velocity a drop of water would acquire in free-fall from the same height: v = sqrt(2gh).
Why is a discharge coefficient (Cd) required in practice?
Real fluids experience friction and flow streamline convergence ('vena contracta') just outside the hole. For a sharp-edged circular orifice, Cd = 0.62, reducing theoretical flow rate by roughly 38%.
Why does draining time take twice as long as constant-velocity draining?
As the liquid level falls, hydraulic head h decreases, steadily slowing the exit velocity. Integrating Torricelli's law over time shows that draining a full cylindrical tank takes exactly twice as long as discharging the same volume at continuous initial velocity.
Does liquid density impact Torricelli exit velocity?
No. In an open atmospheric tank, gravitational acceleration g is identical for all liquids regardless of density (water, milk, oil, or mercury drain at identical theoretical velocities under ideal inviscid conditions).