Flow Rate Through an Orifice Calculator

Equation

$$Q = C_d \cdot A_o \cdot \sqrt{2gh}$$
$$v = \sqrt{2gh}$$
where:

Q = Flow rate through orifice (m³/s)

C_d = Discharge coefficient

A_o = Cross-sectional area of orifice (m²)

g = Gravitational acceleration (m/s²)

h = Vertical distance from water surface to orifice center (m)

v = Velocity (m/s)

Calculator

Property to Calculate:

Flow rate through orifice (Q):

Discharge coefficient (C_d):

Cross-sectional area of orifice (A_o):

Gravitational acceleration (g):

Vertical distance from water surface to orifice center (h):

Velocity (v):

Equation Assumptions

The fluid is incompressible.
The fluid is in steady flow.
The orifice is small relative to the size of the tank, such that the height h does not change significantly as fluid flows through the orifice.
Air viscosity and surface tension are neglected.