Calculator · Fluid Mechanics
Orifice & Torricelli Calculator
Liquid leaving a reservoir through a small opening falls the head above it. Torricelli gives the ideal velocity √(2gh); the orifice discharge is that velocity acting over the opening, scaled by a prescribed discharge coefficient. The two are kept separate on purpose.
Inputs
Measured from the free surface down to the centre of the opening.
Prescribed from the opening's geometry and calibration; it must be positive.
Results
Ideal efflux velocity V = √(2gh)
The velocity the head alone implies, before any coefficient is applied.
| Head h | 2 m |
|---|---|
| Ideal velocity √(2gh) | 6.2631 m/s |
| Discharge coefficient Cd | 0.62 |
| Velocity scaled by Cd | 3.8831 m/s |
Assumptions
- · Large reservoir with a free surface at atmospheric pressure and negligible approach velocity.
- · The discharge coefficient scales the flow rate only; the ideal velocity remains sqrt(2gh).
Explore in the Lab
Each principle keeps its own assumptions in the Lab.
Technical reference
V_ideal = sqrt(2 g h)
Q = Cd A sqrt(2 g h)
- h
- head of liquid above the opening[m]
- A
- area of the opening[m²]
- Cd
- prescribed discharge coefficient, Cd > 0[-]
- Q
- discharge through the opening[m³/s]
A large reservoir with a free surface at atmospheric pressure and a negligible approach velocity. This is not a nozzle or a network model.
A zero head gives exactly zero velocity and zero discharge; a negative head is not a valid state and is refused.
Reference case: h = 2 m, A = 0.01 m², Cd = 0.62 gives an ideal velocity ≈ 6.26312 m/s.