Torricelli's Theorem Calculator

Exit velocity and flow rate from a tank orifice. Derived from Bernoulli's equation assuming the tank surface is large relative to the orifice.

Fluid Mechanics I

Inputs

Fluid height above orifice h (m)

Orifice diameter (optional — for flow rate) d (mm)

Apply discharge coefficient C_d(accounts for real-world losses)

Ideal case (no losses). Real exit velocity is lower — use C_d to correct.

Theory

Ideal exit velocity:

V = √(2gh)

With discharge coefficient and orifice area:

Q = C_d × A × √(2gh)

Where:

h = height of fluid surface above orifice centre [m]
g = 9.81 m/s²
A = orifice cross-sectional area [m²]
C_d = discharge coefficient (0 to 1) — accounts for vena contracta and friction

Derived by applying Bernoulli's equation between the free surface (P = P_atm, V ≈ 0) and the orifice exit (P = P_atm). The result is identical to the velocity of a free-falling body dropped from height h.