A "fractal" modification of Torricelli's formula

作者：Maramathas Athanasios J^*; Boudouvis Andreas G

来源：Hydrogeology Journal, 2010, 18(2): 311-316.

DOI：10.1007/s10040-009-0507-2

• Hydraulic properties
• Karst
• Torricelli's formula
• Darcy's law
• Greece

A modification is proposed of Torricelli's (1608-1647) formula for the velocity of water discharging from a small hole at the bottom of a large tank filled with fractal solid material. The new formula takes proper account of the mechanical energy losses due to flow in the solid matrix, thus expanding the area of validity of the classical Torricelli's formula. Moreover, it offers a convenient alternative to Darcy's law for estimating the discharge rate from an aquifer. The new formula was derived from laboratory experiments, with a low-Reynolds number discharge flow (Darcian flow). It was tested in a natural karst aquifer where the flow is non-Darcian, at Almiros spring on the island of Crete (Greece). In both cases, the predictive capability of the modified formula is established.

• 出版日期2010-3