Pressure Transducer/Tank level information needed

Hello all,
I would like to replace a Ultrasonic Level Sensor with a Presure Transducer for reading the liquid level of a tank in Gallons. The 'ducer will be 4-20mA paired with an AD DL06 PLC. The tank is a capsule shape with a cylinder hight of 65" and a diameter of 34". The conical bottom is approximately 6" high. Max. capacity is 134 gallons. What I need o know is how to figure out what range of 'ducer I need and what type of calculations will be needed to convert to gallons.
Thanks,
Micheal

In addition, you will need to know where your fill and drain lines are located.

The drain line is located on the bottom center of the tank and the fill line comes in about 2" bove the top of the conical portio of the tan bottom.
Micheal

here is link to a PDF for the tank, we re using the 125 Gallon Pedestal Tank.
http://www.terracontanks.com/nav/CMImage.aspx?CMID=0&Name=Terrapure.pdf

There is some relation to inches wg & pressure but can't remember what it is but we have a number of tanks that are 3000-5000 litre tanks & if my memory serves me correct the pd's are 2 bar.
Even if your tank only created 0-200mbar & you used a 0-500 mbar transducer you could still scale it reasonably accurately.
I've no doubt someone here will have a formula & with a conical bottom the only real way would be some clever maths or a lookup table for correction factors for the conical bottom, however if this is for a rough indication of tank level/contents then I would not bother.

There's a reason they call it inches of water.
You will need a sensor that can take at least 70" of water. My Dwyer catalog shows 0 - 100" WC is a standard range.

The calculation to find the volume on a hemisphere has been covered here already. You should be able to find that pretty quickly.

The thing to be careful of, as already inferred, is the inlet and outlet ports. Putting your sensor anywhere near these without a baffle to break up the flow will introduce measurement error due to fluid flow. If you intend to measure all the way down to zero this will be a problem for you given your outlet location unless you are just worried about the static case (no outflow).

Alot of the guys here do more with pressure and flow than I do so they probably have ideas on how to get around this.

Keith

What is the fluid? You need to know that. 1 foot of water will give you .434 PSI. The shape of the tank will not affect the pressure the tank contents exert on the transducer but the contents of the tank (ie, is it water, oil, etc) will affect it. The pressure gives you the height of the fluid in the tank and then basic geometry will allow you to convert it to gallons. If you need precise measurements then you will also need to know the temperature of the fluid.

Originally posted by Alaric:

What is the fluid?

Click to expand...

You're right. I made an assumption I shouldn't have.

Keith

Thanks for the info, the fluid is water and it will be between 68-77 deg F. Also the tank hight is 28" not 65". So my Max hight of water will be around 34"/12=2.833 ft X .434=1.2296 PSI....correct?

We use 3"/150# flange mounted PT's for tanks having thick, viscious fluids in them, and smaller 2" remote-seal ("pancake style") meters for tanks with thinner liquids.

In ALL cases the HIGH side is mounted down near the bottom of the vessel, and the LOW side (typically 1/2" tubing impulse line or remote seal) is connected to the top to compensate for vapor pressure.

The formula we use to calibrate the meter is: "height(in inches) x SpecGrav. of the liquid"

Specific gravity is dependant somewhat on the temperature of the liquid inside and can throw off your inventory one way or the other--a safety margin at the top of the vessel should be considered for expansion.

The taps for the meters are subject to routine fouling, as they are dead-headed, and generally have to be insulated/heat-traced if you live in the Midwest or other areas subject to cold weather. They also need to be blown down on occassion, which may require additonal procedures and permitting depending on what you're making.

Using PT's in this manner to replace old mechanical, float-style LT's (such as Mason-Neilan units) has worked out great for us, but if you need a higher degree of accuracy then I'd look at loop-powered radar or another solution similar to that. PT's will never give you a high degree of accuracy.

Head pressure is affected by movements of the liquid oontents because those movements have a force and pressure is force/area.

Head pressure can not 'see' any level below the elevation of the sensor.

That means that to measure with head pressure, you need to sense at a point below the lowest level, and that such a point should not be influenced by things like flow passing by the sensing point, which will affect the pressure reading you want to be 'level' only.

Do you have an access point on the bottom of the tank that is not the outlet/drain?

Sometimes, 'smart' transmitters are needed in order to apply an offset to zero correct for head pressure that isn't true level pressure, but pressure from liquid in impulse lines or pressure artifacts due to the transmitter not being plumb or level.

Head pressure is typically measured in inches of water column.

If you fluid is water, then the reading is a direct reading. If the fluid hsa some other density (specific gravity SG), then the inches of w.c. value has to be corrected by the S.G.

The range needed is the sum of the distance from upper level to lower level, plus any amount needed if transmitter is mounted below the low level elevation, times (multiplied by) the specific gravity of the fluid. The diameter has zero influence on a head pressure calculation.

In your example:
65" tank height
plus 6" cone depth
equals 71" times specific gravity of fluid.

If the SG were 1.05, then 71 * 1.05 = 74.55" which is what the transmitter outputs.

On the PLC end, you have to divide by the SG to get back to physical level or distnnce.

The conversion to gallons needs either a polynomial or a look-up table correction to take the volumen in the cone level into account.

1psi = 27.7inwc

Calculating the volume takes two steps.

The volume of a cone is pi/3*r^2*h. But in a conical tank the diameter of the cone changes with fluid height. So we subsitute tan X * h for the radius of the cone.

Thus, volume in the conical portion of your tank is given by

pi/3 * (tan X * h)^2 * h

where X is the angle the conical portion of the tank makes from the vertical axis of the tank, and h is the fluid height in the cone.

For your 34" diameter tank with a six inch conical sectcion, (assuming those are tank interior dimensions, then the angle of the cone from vertical is 70.56 deg. The volume of the cone is given by
pi/3*(tan 70.56 * h)^2 * h
simplifying:
V = 8.4067 * h^3. If the cone angle is something different than 70.56 then you need to recalculate.
To convert that to gallons, 1 gallon is 231 in^3, so
gallons = .03639265 * h^3

For heights above 6" the tank volume is the total volume of the cone + the volume of the cylinder above the cone. The total volume of the cone, from above, is 7.861 gallons. A cylinder volume is given by pi()/4*d^2*L where d is the diameter and L is the cylinder length.

In your tank, pi()/4 and d^2 are fixed values, so combining the constants for your tank we get 907.92 * L. Since we have a six inch cone on the tank, then L which is total fluid column height - 6. Converting to get gallons (1 gal=231 in^3) we have 3.9304 * (h-6).

Summarizing:
If fluid column height is <= 6" then gallons := .03639265 * h^3
If fluid column height is > 6 then gallons := 7.861 + (3.9304*(h-6))

note: h * h * h computes faster than h**3, something to consider when you go to program this.

edit to add: Conical bottom tanks with drains attached at the cone are usually not really conical, but are actually frustrums, that is a cone with a flat instead of a point, then you have an additional cylinder which is the pipe from the bottom of the frustrum to the valve. Keeping in mind the actual physical location of the sensor, it is up to you to determine how this impacts the accuracy of your volume calculations, but hopefully you can see from what we have covered how to do that.

Maybe I am missing something here but here are my figures.

28" Tall by 34" Width with a 6" cone = 117.9 with the cone volume at 7.8 gallons.

I have always started with a empty tank, take your 4-20 ma reading.
Fill the tank, take your 4-20 ma reading and then scale that in the plc to your gallons.

Mark Buskell said:

...here are my figures.

28" Tall by 34" Width with a 6" cone = 117.9 with the cone volume at 7.8 gallons.

Click to expand...

Nope, you're not missing anything. Those figures are right, which is a little less than the 134 gallons from earlier. 134 gallons would be the volume of the tank if it were a simple cylinder without the conic bottom.

The suitability of simple linear scaling depends on the accuracy needed. For basic indication its probably more than adequate, but for process/quantity control it probably isn't. In evaluating the suitability of simple linear scaling we should be cognizant that a conical tank is not linear.


This is a graph of the volume of fluid of a conical bottom tank -vs- fluid height - as you can see, its non-linear as fluid height rises through the conic section.

You americans, still on feet, inches & gals.
We british oldies tried our best to not use metric but it makes sense now.
wouldn't do it any other way