## Differential pressure in open tank level measurement

Pressure, pressure, and more pressure! As we said in the article about absolute, gauge, and differential pressure, we can use a pressure device to measure other process variables like level and flow. It sometimes amazes me how many processes and segments use pressure transmitters, probably because people don’t know of better solutions. Still, we always have a hard time saying no to easy and cheap answers.

In fact, we know enough to apply a differential pressure (DP) transmitter to level measurement quickly. On the downside, pressure solutions come with a long list of limits and problems we could avoid with newer solutions.

Because I’m sure our newer members in the community have questions related to level calculation and transmitter installation, I proffer an article to explain DP level measurement and the math behind it.

So let’s math!

### Level measurement

We base DP level measurement on the Pascal equation for hydrostatic pressure. Therefore pressure (P) equals the liquid’s density (ρ) times acceleration due to gravity (g) times the liquid column’s height (h), or P = ρ * g * h.

Although different processes may call for more complicated calculations, don’t worry. You can build from here and learn as you go. With that in mind, let’s go through a simple situation now, an open tank process, and later we can go to a more complicated one.

### Open tank

First, we need to talk about how DP transmitters work. Here you have two cells, one for high pressure and one for low. Pay attention, because you must know this to install the transmitter properly!

With level measurement based on hydrostatic pressure, the high-pressure cell goes at the bottom of the tank. And in an open tank, the low-pressure cell should be open to the air.

Some companies sell gauge transmitters for open tanks. A gauge transmitter will work fine, but instead of having the low cell open to the air, you have just a vent in the transmitter.

### Level measurement in open tanks

In this setup, we have a transmitter installed at the tank’s zero level, dead easy. Also, you have the level connection filled with the process product. Still with me?

So you just need to figure the minimum and maximum measurements.

Minimum = level at 0% = HP (SGp * H) – LP (SG * H)

Maximum = level at 100% = HP (SGp * H) – LP (SG * H)

- HP = high pressure
- LP = low pressure
- SGp =
**Specific**gravity of process - H = height

Here, the minimum will always equal zero because you have zero on both sides. On the 100 percent, you multiply the height of the liquid in the full tank with the gravity for the high pressure. For the low pressure, you’ll still have zero, so you can leave it.

### Open tank with suppressed zero installation

Now, let’s try a different installation, with the transmitter below the zero level. Because the transmitter shows a value higher than the real value, we call this suppressed zero. Our scenario has a transmitter without a seal pot and the process connection filled with the process product. Later, we’ll calculate the same level with a seal pot.

We’ll use the same equation, but we need to pay attention to the new height with the transmitter below the bottom of the tank.

Minimum = level at 0% = HP (SGp * h1) – LP (SG * H)

Maximum = level at 100% = HP (SGp * h1 + H2) – LP (SG * H)

- HP = high pressure
- LP = low pressure
- SGp =
**Specific**gravity of process - H= height
- h1 = height of the suppressed zero
- H2 = height of the full tank

Does that make sense? Next, imagine a situation where you have a seal pot on the HP side of the transmitter. Because the seal pot’s density differs from the process product, this difference will add to your math. Take a look!

Minimum = level at 0% = HP (SGs * h1) – LP (SG * H)

Maximum = level at 100% = HP [(SGs * h1) +( SGp * H2)] – LP (SG * H)

- HP = high pressure
- LP = low pressure
- SGp =
**Specific** - SGs =
**Specific** - H= height
- h1 = height of the suppressed zero
- H2 = height of the full tank

### Conclusion

Thus, you start with an easy equation and build on it. However, we always need to pay attention to each detail in the setup. Otherwise, you may set up with the wrong range or wrong zero references and get wrong results.

**If you want to read more about level measurement at Visaya, check these out:**

**1.Hybrid level measurement!: ***Hybrids! And we ain’t talking cars here. Yeah, certain applications need hybrid level transmitters, like the FMP55, for hybrid level measurement. That device gives you a combo of guided radar and capacitive level transmitter. Buy one, get one free, and everybody loves BOGOs!* Read more

**2.Differential pressure transmitter applied in a level measurement:** *Before anything else, there’s something you should know: There are better technologies than a differential pressure transmitter on the market today that you can use for level measurement.*

*However, you need to figure out your budget for your application. That way, you can figure out if a differential pressure transmitter will provide you with enough information and if the accuracy is enough for your application.* Read more

3.**Cryogenic level measurement: ***Good question about cryogenic level measurement! So, most applications hold liquids with below-freezing boiling points, such as nitrogen and methane, in thermally insulated vertical tanks. Still, the tank will always have a gas pressure head for the liquid vapor. Also, these fluids have low oxygen permeability, or Dk values, which make radar devices a poor choice.* Read more

**4.Radar level measurement: ***So you’re wondering how radar level measurement works? We can certainly explain this. Radar level meters work based on the time of flight (TOF) method or time domain reflectometry (TDR). To start with, you measure the distance from the reference point to the surface of your liquid. Then the meter sends a high-frequency signal from an antenna or along a probe.* Read more

*This article is part of our Book of Instrumentation. To learn more about Process Instrumentation check out the whole book here.*