Torricelli Law Calculator
Find tank exit speed, drain time, and volume from diameters and depth.
What it does
A hole near the bottom of a tank shoots water with the speed of a matching free fall. Depth alone sets that speed: the deeper the water above the hole, the faster the jet. Tank width never enters the speed, but it decides how long the show runs by fixing how much water waits behind the hole.
The tool above runs both halves. Enter tank diameter, hole diameter, and starting depth in metric or imperial to get exit speed, full drain time, and tank volume. Defaults describe a 1.0 m tank with 1.5 m of head over a 20 mm hole, so the page opens solved at 5.42 m/s, 23 min, and 1,178 L.
The square in the time formula deserves respect. Drain time grows with the square of the diameter ratio, so halving the hole quadruples the wait. The example ratio of 50 squares to 2500, and each of those 2500 units costs the 0.553 s free fall factor, totaling about 1382 s.
Both modes mirror cleanly: 3.28 ft, 0.79 in, and 4.92 ft give 17.80 ft/s with 311.0 gal behind it. Practice runs show the spread: a small 0.5 m tank at 1.0 m head exits at 4.43 m/s and empties in 18.8 min, while imperial branches reach 13.90 ft/s and 70.5 gal.
Use the table for common hole sizes on the example tank, then run your vessel. The page assumes straight walls, a sharp clean hole, no inflow, and a coefficient of 1, so real tanks with screens or valves drain slower. Within range it sizes drain down tests and overflow checks fast.
How to use
- Pick metric or imperial.
- Enter tank diameter and hole diameter.
- Enter starting water depth.
- Read exit speed first.
- Read drain time and tank volume.
- Derate for screens, valves, and inflow.
Formula
- D
- Tank diameter: m metric, ft imperial.
- d
- Hole diameter: mm metric, in imperial.
- H
- Starting water depth above the hole.
- g
- Gravity: 9.81 or 32.2 in matching units.
g is 9.81 metric or 32.2 imperial with matching length units. H is the starting depth above the hole and the tank is assumed straight walled with no inflow. Real holes discharge less than theory through a coefficient the page leaves at 1, so treat times as best case.
Worked example
Example: 1 m tank draining through 20 mm
A straight wall tank of 1.0 m diameter holds 1.5 m of water above a 20 mm hole. Find exit speed, drain time, and volume.
- Exit speed = sqrt(2 x 9.81 x 1.5) = sqrt(29.43) = 5.42 m/s.
- Diameter ratio = 1.0 / 0.02 = 50; squared = 2500.
- Time factor = sqrt(2 x 1.5 / 9.81) = sqrt(0.306) = 0.553 s.
- Drain time = 2500 x 0.553 = 1382 s, shown as 23 min.
- Volume = pi/4 x 1.0 squared x 1.5 = 1.178 m3, shown as 1,178 L.
- Imperial mirror gives 17.80 ft/s and 311.0 gal.
Reference table
| Hole | Exit speed | Drain time |
|---|---|---|
| 10 mm | 5.42 m/s | 92.2 min |
| 20 mm | 5.42 m/s | 23 min |
| 30 mm | 5.42 m/s | 10.2 min |
| 40 mm | 5.42 m/s | 5.8 min |
Limits
- Straight wall tanks with no inflow.
- Sharp hole with coefficient 1 assumed.
- No viscosity, screens, or valves.
- Best case times; real drains run slower.
Common mistakes
- Mixing mm with meters in the ratio.
- Reading speed as the drain time.
- Forgetting the square on D/d.
- Using depth below the hole.
- Trusting theory with a clogged screen.
Try it yourself
Quick checks. Answers sit tucked under each question.
Small tank: 0.5 m diameter, 10 mm hole, 1.0 m head?
Exit 4.43 m/s. Drain 18.8 min. Volume 196 L.
Imperial: 2 ft tank, 0.5 in hole, 3 ft head?
Exit 13.90 ft/s. Drain 16.6 min. Volume 70.5 gal.
1.0 m tank with a 25 mm hole at 1.5 m head? Work it by hand.
Ratio = 1000/25 = 40, squared 1600. Time = 1600 x sqrt(3/9.81) = 1600 x 0.553 = 885 s, about 14.7 min.
Questions
What is Torricelli law?
The tank drain rule from Bernoulli: exit speed equals sqrt(2gh) with h the depth above the hole. A straight wall tank drains in (D/d) squared times sqrt(2H/g).
Does tank width change exit speed?
Speed depends only on depth, not on tank width. Width sets volume and therefore drain time, which grows with the square of the diameter ratio.
Does it work in feet and gallons?
Yes. Pick imperial: 3.28 ft tank, 0.79 in hole, 4.92 ft depth gives 17.80 ft/s and 311.0 gal.
How is drain time formatted?
Times under two minutes print in seconds, longer runs in minutes, and very long drains in hours.
Does it assume a sharp hole?
Yes, for a sharp clean hole. Rounded inlets, screens, and partial valves cut the real flow below theory.
Is it exact for real tanks?
No. Viscosity, inflow during draining, coned bottoms, and long outlet pipes all break the simple form.