Time to Empty or Drain a Tank, Pond, Reservoir Containing Water or other Liquid
Compute time to empty (or lower) water or other liquid. Also can solve for discharge coefficient, orifice diameter (or area), tank diameter (or area), initial liquid depth, final liquid depth.
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Units: cm=centimeter, ft=foot, hr=hour, m=meter, min=minute, sec=second.
Tank (or pond or reservoir) is open to the atmosphere. The tank can be cylindrical or other cross-section but must have the same cross-section for its entire height. The orifice can be circular or non-circular. If tank or orifice is non-circular, enter their area into our calculation. Hi , Hf , and h are measured vertically from the centerline of the orifice.
Note: The above equation is valid if both the tank and orifice are at the same pressure, even if the pressure is not atmospheric
For a tank with a constant cross-sectional geometry A in the plan view (i.e. as you look down on it), substitute:
Integrate h from Hi to Hf and integrate t from 0 to t, then solve for time t, which is the time required for the liquid to fall from Hi to Hf:
If the tank is circular in plan view (i.e. looking down on it):
If the orifice is circular:
Our calculation allows you to solve for any of the variables: C, d, a, D, A, Hi, Hf , or t. The orifice and tank can be either circular or non-circular. If non-circular, then the diameter dimension is not used in the calculation.
The tank and orifice discharge are assumed to be at the same pressure.
The tank is assumed to be of sufficiently larger area than the orifice so that friction effects from the tank wall are negligible; that is, A>10a as a rule of thumb suggested by LMNO Engineering.
Orifice Discharge Coefficient
Type: Rounded Sharp-edged
Short tube Borda
The short tube value is valid for L ~ 2.5d. Borda is also known as "re-entrant" since it juts into the tank.
Error Messages given by calculation
"Need Hi > Hf". Initial depth must be larger than final depth.
"Best if A ≥ 10a". To ensure that tank friction is negligible, should have tank area much larger than orifice area.
"Need 0 < C ≤ 1". Discharge coefficient must be greater than 0.0 and less than or equal to 1.0. Typical value is 0.6 for water flowing through square-edged orifice.
"Infeasible input". This message can occur if the final depth is being computed and Hi0.5 < [t a C (g/2)0.5] / A
Daugherty, R. L., J. B. Franzini, and E. J. Finnemore. 1985. Fluid Mechanics with Engineering Applications. McGraw-Hill, Inc. 8ed.
Streeter, V. L., E. B. Wylie, and K. W. Bedford. 1998. Fluid Mechanics. McGraw-Hill, Inc. 9ed.
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LMNO Engineering home page (more calculations)
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