Torricelli's Law

Torricelli’s law tells you the exit speed of a liquid jet coming out of a small hole when the fluid surface is open to the atmosphere. It comes from applying conservation of mechanical energy to a fluid parcel: the loss in gravitational potential energy from falling a vertical distance h is converted into kinetic energy, giving v = sqrt(2gh). The result assumes an ideal fluid with negligible viscosity, a small orifice, and a large tank so the surface speed is tiny compared with the outflow speed.

Use this when you need the speed of liquid leaving a tank, reservoir, or container through a small hole at a known depth below the free surface. It is common in fluid mechanics problems involving draining tanks, jet trajectories, and idealized efflux from openings.

• Using the depth below the top of the tank incorrectly by measuring from the hole to the bottom instead of to the free surface
• Forgetting that h must be in meters and g in m/s^2 so the speed comes out in m/s
• Applying the formula to large, viscous, or pressurized flows without checking the ideal-flow assumptions