# How to Calculate the Time to Drain a Tank

Written by mark koltko-rivera
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The basic factors to consider in draining a tank filled with liquid--whether it is a septic tank, an oil supertanker, or the fuel compartments of a giant rocket--are the same: tank volume and flow rate.

Skill level:
Moderate

### Things you need

• Physical dimensions of the tank
• Estimated or observed flow rate
• List of formulas for volumes of three-dimensional objects (cylinder, sphere, cube, prism)
• Calculator

## Instructions

1. 1

Determine the capacity of the tank. This capacity may be written on the tank itself, or noted elsewhere, such as on a meter or counter. If you can determine the capacity of the tank in this manner, skip Step 2.

2. 2

Calculate the volume of the liquid in the tank. If the tank is a simple shape, like a cylinder or a sphere, use the standard formulas for volume for these shapes. If the tank is irregularly or unusually shaped, make a drawing of the tank and divide it into a series of spheres, cylinders, prisms, and/or pyramids, and use the standard formulas for those shapes to approximate the volume of the tank; see Clark, or chapter 4 of Harris and Stocker.

3. 3

Divide the volume of the liquid in the tank by the estimated or observed flow rate. The result is the time it takes to drain the tank.

#### Tips and warnings

• This presentation assumes a steady or constant flow rate, such as one might encounter with using a pump. However, if one is draining a tank by simply opening a portal in or near the bottom of the tank, using gravity to force the liquid out, then the flow rate will vary depending on how much liquid remains. The mathematics for describing flow rate that varies over time are considerably more complicated than what is presented here. As a rough guideline, one might estimate this using the flow rate observed when draining a tank like this at half-empty.
• This presentation also assumes that the tank is full at the beginning. Of course, if only a fraction of the tank is full when you begin to drain it, you must adjust your calculations accordingly: For example, half a tank should take about half the time to drain that a full tank does.

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