# Calculating diesel volume in a horizontally-cylindrical tank

This is about several diesel tanks that need to be monitored in terms of diesel volume. I want to measure and monitor the volume of Diesel liquid inside horizontally cylindrical tanks with standard dimensions, however the safety rules are strict, where no electrical devices or wires has to exist in the tank zone, which limits the solution to few methods or devices. What i want to achieve is to measure the diesel volume inside the tank without having to use an ultrasonic sensor, as it will require some modification to the tank, not mentioning the wires connecting from the transducer to the display unit. the question here is whether we can use a sensor that can be attached to the output pipe of the tank and calculate the diesel volume. a sensor to measure pressure or flow, will it work for such requirements ? If yes, how do I calculate the volume based on those values ? and is there's any device in the market that can provide the volume of liquid inside the tank straight forward without the need to make any further calculations using the outlet pipe ? The tank is similar to the one in the picture below. Thank you.

• Put a “tee” in the outlet pipe and use a vertical pipe : the liquid level in the pipe will match the tank level as long as the flow is low... neat non-electrical solution as required and not in the tank either... – Solar Mike Mar 21 '18 at 11:12
• @SolarMike could you share a link for such device – lightworks Mar 21 '18 at 12:20
• Search for pictures of tanks - this is a classic solution... – Solar Mike Mar 21 '18 at 12:22
• See this related answer for a list of common level measuring techniques. engineering.stackexchange.com/a/2746/33 – hazzey Mar 21 '18 at 12:41
• For your calc, you seek Volume of a Horizontal Cylinder Segment. – StainlessSteelRat Mar 21 '18 at 13:17

There is an explicit formula to calculate the cross-sectional area $A$ of a segment of a circle, and therefore the volume $V$. of the liquid The tank is filled to the height $x$ (measured from the bottom).

The cross-sectional area is given by: $$A=\mbox{arccos}\left(\frac{R-x}{R}\right)R^2-(R-x)\sqrt{2Rx-x^2}$$ The volume $V$ is just: $$V=A\cdot L$$ Now, I assume you would probably rather measure $d$, the distance of liquid level from the top, thus you would have to replace $x$: $$x=2R-d$$

This is completely standard tank measurement.

First of all, diesel is hardly a very flammable liquid. Second, electrical atmosphere in flammable installation is a well known thing. We have a standard for it - ATEX.

Get a compliant pressure sensor, or float sensor, and mount on a flange on the outlet pipe, or a flange on the tank if available. Danfos MBS3000 can for instance be used. Correctly installed this is perfectly safe.

I'd be surprised if ultrasounds are not made with ATEX specification as well.

Use the formula $$A = (R^2/2)*(\theta - sin\theta)$$

And $$R-H = cosa$$ and $$a =\theta/2$$ A is the surface of Diesel liquid inside the tank.

R is the radius of the tank.

H is height of fuel in the tank.

$\theta$ is the central angle between the 2 sides of section made by fuel to center of the tank. Once you find A the volume is,

$V= A.L$

L is length of tank.