Time to Drain a Conical Tank Equation and Calculator

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Time to Drain a Conical Tank Equation and Calculator

Fluids Flow Design and Engineering
Hydraulic & Pneumatic Design Engineering
Pressure Vessel Engineering

Efflux Time to Drain a Conical Tank Equation and Calculator

The conical tank, with dimensions given in the figure 1, is initially filled with a liquid. The liquid is allowed to drain out by gravity. Viscosity losses are being ignored in formulas and calculator. Efflux time or time to drain is given by.

Eq. 1
t_efflux = ( 1 / 5 ) · ( z_o / z₂ )² · ( 2 · z_o/g )^0.5

Where:

z_o = Vertical Coordinate at the Top of the Cone (m)
z₂ = Vertical Coordinate just Above the Datum Plane for Potential Energy (m)
g = Gravitational Acceleration (m/s²)
t_efflux = Efflux Time (s)

Figure 1
Conical container from which a fluid is allowed to drain. The quantity r is the radius of the liquid surface face at height z, and r average is the radius of the cone at some arbitrary height Z.

Source:

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 7, Page: 229.