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How This Is Calculated


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

Q   =   Flow rate through orifice   (m³/s)

Cd   =   Discharge coefficient

Ao   =   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)


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.


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