Orifice Discharge Calculator
Enter discharge coefficient, orifice area and head to compute the discharge Q = C_d·A·√(2·g·h).
Input Data
Results
At a glance:Flow through an orifice is given by Torricelli's law extended with a discharge coefficient: Q = C_d·A·√(2·g·h), where A is the orifice area, h the head (height of fluid above the orifice center), g gravity and C_d the discharge coefficient (accounts for contraction and viscous losses; ~0.61 for a sharp-edged circular orifice, higher for rounded). The ideal (C_d=1) velocity is v = √(2gh), the speed a freely falling body reaches from height h. This applies to tanks draining under gravity; time to empty integrates Q over decreasing h. This tool returns Q from C_d, A and h.
Formula
Q = C_d·A·√(2·g·h)
Ideal velocity: v = √(2·g·h)
$$Q = C_d\,A\,\sqrt{2\,g\,H}$$How to Use
- Enter the discharge coefficient C_d.
- Enter orifice area A (m²) and head h (m).
- The calculator returns discharge Q.
Case Studies
Tank drain
C_d = 0.61, A = 0.001 m², h = 2 m.
Q = 0.61×0.001×√(2×9.81×2) ≈ 0.0038 m³/s.
About 3.8 L/s.
FAQ
What is the discharge coefficient?
C_d corrects the ideal Torricelli flow for the vena contracta (jet contracts) and friction; for a sharp-edged orifice C_d ≈ 0.6, for a well-rounded one closer to 1.
Why √(2gh)?
It is the speed from converting hydraulic head h to kinetic energy (Bernoulli): v = √(2gh), the same as a body falling distance h.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.