BIZOMAT MAKEOS · Hydraulics
Tank Drain Time Check (Volume Drained, Initial Outflow, Time Through an Orifice)
How long will this vertical tank take to drain from one level to another through a bottom outlet, and what outlet size would drain it in the time I want?
Drain time of a vertical cylindrical tank through a bottom orifice or short outlet: the volume between the two levels (as the tank volume tool), the outflow at the starting level from the head as a pressure drop (as the orifice flow tool), the time to fall from the starting to the final level with the head falling as the tank empties, and the outlet diameter that would drain it in your time, against the time allowed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tank inside diameter | mm | Inside diameter of the tank. |
| Starting level above the outlet | mm | Liquid level above the outlet at the start. |
| Final level above the outlet | mm | Liquid level above the outlet when draining stops. |
| Outlet diameter | mm | Outlet diameter. |
| Discharge coefficient | Discharge coefficient of the outlet (about 0.6 for a sharp orifice, 0.8 for a short pipe). | |
| Liquid density | kg/m³ | Liquid density (for the outflow as a pressure drop). |
| Time allowed | min | Time the drain must take at most. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Tank inside diameter
- What it is
- The inside diameter of the vertical cylindrical tank, which sets the liquid volume per millimetre of level.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drain time rises with the square of the tank diameter.
- Get it right
- Use the inside diameter; the outside diameter overstates volume and drain time.
What this means: Starting level above the outlet
- What it is
- The height of the liquid surface above the outlet when draining starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure to the outlet centre line, not to the tank floor.
What this means: Final level above the outlet
- What it is
- The height of the liquid surface above the outlet when you consider the drain finished.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be below the starting level; the last part of the drain is the slowest.
What this means: Outlet diameter
- What it is
- The diameter of the outlet opening through which the tank drains.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drain time falls with the square of the outlet diameter.
- Get it right
- Use the narrowest bore in the outlet, such as a valve port, not the pipe nominal size.
What this means: Discharge coefficient
- What it is
- The ratio of the actual outflow to the ideal outflow through the same opening, allowing for jet contraction and friction.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Drain time falls in direct proportion as the coefficient rises.
- Get it right
- Choose it for the outlet shape from a fluid-flow reference or the valve maker; valves and long pipes lower it.
What this means: Liquid density
- What it is
- Mass per cubic metre of the liquid. Here it only converts the starting head into a pressure for the report; drain time and outflow do not depend on it.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the density at working temperature from the liquid data sheet.
What this means: Time allowed
- What it is
- The longest time the drain may take, compared with the calculated drain time.
- Units and format
- Enter a number in min: minutes. The form accepts 0.000001 min to 1000000 min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter minutes, not seconds.
Method and formulas
- Volume = π D² (H₁ − H₂) ÷ 4 (as the tank volume tool).
- Outflow at the start Q = C_d A √(2 Δp ÷ ρ) with Δp = ρ g H₁ (as the orifice flow tool).
- Time t = (A_tank ÷ C_d A_outlet) √(2 ÷ g) (√H₁ − √H₂); the outlet for a time t₀ is d √(t ÷ t₀).
- Example: 1,583.4 L drains in 26.258 min; a 23.389 mm outlet would meet the time allowed.
Limitations
- Unrestricted outflow to air from a tank open at the top; a vented, pumped or piped outlet changes the flow.
- Outlet losses taken in the discharge coefficient; long drain pipes need the pipe friction tool.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find how long a tank takes to drain for cleaning
- Size a drain outlet for an emergency dump
- Estimate outflow from a tank at a given level
Who it is for
- Process engineers
- Plant operators
- Maintenance engineers
What you get
- Volume drained
- Outflow at the start
- Drain time and outlet for the time allowed
Interpreting the result
- The last part of the tank drains slowest because the head is lowest; draining fully takes far longer than draining half.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 68–69, 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Froude scaling: flows, velocities, times and forces
In Scale Models by the Numbers
What it covers: Derive the Froude scaling ratios for velocity, flow, time, pressure, force and power, apply them to the PS-3 model, and check them on a draining tank and an orifice.
Method explained here · BIZOMAT original book
Time steps, accuracy and Heun's method
In Simulating Noisy Systems by the Numbers
What it covers: Why a nonlinear drift makes the time step matter, Heun's predictor–corrector step, checking the deterministic part against an exact drain time, and choosing the step by a convergence test.
Useful alongside · BIZOMAT original book
Bulk solids are not liquids
In Bulk Solids Flow by the Numbers
What it covers: Why a powder or pellet store carries load by friction and force chains, so its pressures level off with depth and its discharge rate does not depend on how full it is.
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Open the Tank Drain Time Check (Volume Drained, Initial Outflow, Time Through an Orifice) calculator