How to use the tank drain time calculator
- Pick the tank shape: a vertical cylinder, a rectangular box or a cone with its point down.
- Enter the tank size, the starting liquid depth above the opening and the ending depth.
- Enter the size of the opening and the discharge coefficient in More options.
- Read the drain time, the flow rate at the start and end, and the time to reach each depth.
Formula
Exit speed v = sqrt(2 g h); flow Q = Cd x a x sqrt(2 g h)
Straight sides: t = A / (Cd a sqrt(2g)) x 2 (sqrt(h1) - sqrt(h2))
Cone, point down: t = pi (R / H)^2 / (Cd a sqrt(2g)) x (2/5)(h1^2.5 - h2^2.5)
Volume drained: A x (h1 - h2) for straight sides; pi (R / H)^2 (h1^3 - h2^3) / 3 for a cone
A is the surface area of the liquid, a the area of the opening, Cd the discharge coefficient, h1 and h2 the starting and ending depths above the opening and g is 9.80665 m/s^2.
A barrel, a tank and a hopper
A cylindrical barrel 0.6 m across filled to 0.9 m, draining through a 25.4 mm hole with Cd = 0.61, empties in 391.9 seconds, which is 6 min 32 s. It holds 254.47 liters and the flow starts at 1.299 liters per second. After 52.5 seconds a quarter of the depth is gone, but the last tenth takes over 2 minutes.
A box 2 m by 1 m draining from 1.2 m down to 0.2 m through a 1 inch hole takes 1894.2 seconds, 31 min 34 s, and moves 2000 liters. A cone-shaped hopper 1 m across and 1.5 m tall, full, draining through a 30 mm hole empties in 201.5 seconds.
Why draining slows down
The flow depends on the square root of the depth, so as the level falls the flow falls too. A tank takes as long to lose the last quarter of its depth as it does the first three quarters together. The table of times shows this, and it is the reason a barrel seems to drain quickly at first and then dribble.
For the capacity of the tank itself use the tank and cylinder volume calculator. Other flow tools are the flow rate calculator, the pipe volume calculator and the French drain calculator.
The discharge coefficient
A real jet narrows just after it leaves a sharp-edged hole, so the flow is less than the ideal. The discharge coefficient Cd corrects for that. About 0.6 is common for a sharp-edged round hole, but a rounded entrance gives a higher value, and a pipe, valve or tap changes everything. The value shown is an example, so replace it with one that matches your outlet.
Assumptions and limits
- The tank is open at the top, the liquid is water-like and thin, and the head above the opening is the only driving force.
- No air restriction, pipe friction, valves or inflow are modeled. Long pipes make real draining slower.
- The opening is small compared with the tank and the flow is steady at each depth.
- The cone has its point down at the opening, and the depth is measured from the point.
Frequently asked questions
How do I calculate the time to drain a tank?
Use Torricelli's law: the time is the tank's surface area divided by Cd times the opening area times the square root of 2g, multiplied by 2 times the difference of the square roots of the starting and ending depths.
Why does the last bit take so long?
As the depth falls, so does the pressure pushing the liquid out. The flow slows toward zero, so the last few centimeters take far longer than the first.
What discharge coefficient should I use?
For a sharp-edged round hole, around 0.6 is the usual starting point. Rounded openings are higher, near 0.9 or above, and openings with fittings differ. Measure one drain time and adjust Cd to match.
Can I find the flow rate too?
Yes. The starting flow is Cd x a x sqrt(2 g h1), and the page shows it in liters per second and gallons per minute, along with the average and the ending flow.