# Torricelli-Bernoulli sign

Last revised by Yuranga Weerakkody on 11 Dec 2023

The Torricelli-Bernoulli sign denotes non-dependent air trapped in a necrotic ulcer in a gastrointestinal tumor seen on axial CT or MRI. Occasionally, a vertical stream of bubbles can be seen issuing from the orifice of the ulcer.

Torricelli's theorem gives the relation of the velocity of a fluid flowing from an opening to the distance from the fluid's surface. The speed is not influenced by the direction of flow. This is the speed of a drop of water falling freely under the force of gravity alone, disregarding friction. Torricelli's theorem is actually a particular case of Bernoulli's principle.

Bernoulli's principle states that a fluid's speed is inversely proportional to its pressure and potential energy. It holds true only for an incompressible fluid with an unvarying flow and negligible friction. The principle can be transferred to gases under certain conditions.

This phenomenon occurs if the ulcer is above an air-fluid level with the patient upright, then under fluid after the patient switches to a recumbent position (i.e. for the imaging examination).

The Torricelli theorem was discovered by Italian physicist and mathematician Evangelista Torricelli in 1643 and was later incorporated into Bernoulli's principle, published by Swiss physicist and mathematician Daniel Bernoulli in 1738.

The "Torricelli-Bernoulli sign" was coined in 1999 by radiologist Brian J Fortman 1.