Formula for irregular tank dipstick

[rodfishsa]

G'day
I hope I'm not posting inappropriately, I did read on any topic but if this site is only for students just let me know and I'll ask elsewhere.
I've been trying to work out an accurate way to calibrate a dipstick for my boats fuel tanks. I would like to mark a dipstick in 10L increments so when the boat on trailer is all level I can calculate fuel usage fairly accurately.
If you can point me in the right direction that would be appreciated
Cheers
Rod
Adelaide

 

[stapel]

....if this site is only for students just let me know....

This is a tutoring forum, where students post homework questions and math helpers reply with suggestions, links, etc, to assist the students in getting "un-stuck". If you're needing engineering assistance, this might not be the best place to obtain such.

That said, I'm not sure that the drawing provides sufficient information. For instance, what is the meaning behind the division of the large rectangular-ish prism (the "tank"?) into three sections of 300-units width (plus a fourth which, I think, is meant to be 310 units wide)? What are the "units"? (Millimeters? Inches? Something else?) What is the significance of the "sender unit"? Are the stated dimensions mathematical ideals (so there are no wall-width considerations)? If not, are these interior or exterior measurements? Is the base of the prism (rather than the trailer supporting the prism) assumed to be level? If not, what is the angle from the horizontal? At what point is the dipstick meant to be inserted?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[Ishuda]

G'day
I hope I'm not posting inappropriately, I did read on any topic but if this site is only for students just let me know and I'll ask elsewhere.
I've been trying to work out an accurate way to calibrate a dipstick for my boats fuel tanks. ...

Hey Rod,

You can go through the exercise of doing the measurement and calculations or you can just 'do it'. Build your tank, get 'things' set up [level or maybe canted a bit or ...], note the set up and start pouring in liquid [actually you could use water before it was installed for a set of measurements if you make sure to let it dry well before installing and filling with fuel]. At 10L, wait 'a bit' so that the baffle plates have let things settle out and measure the level and mark it. Repeat as necessary.

You might want to do this for a couple of configurations so you can get an idea of what a small amount of tilt will do to the measurement. Use different dip sticks or maybe different colors of paint to mark the stick if the difference is significant.

 

[stapel]

You can...just 'do it'....

Ah, yes; the simplicity of a "real life" solution, versus the messiness of the "ideal" mathematical solution. Nicely done!

 

[Ishuda]

Ah, yes; the simplicity of a "real life" solution, versus the messiness of the "ideal" mathematical solution. Nicely done!

Oh, I worked it through anyway, using a couple of assumptions, since I like numbers and I would do it both ways 'just because'.

 

[rodfishsa]

Thanks for the replies. Sorry for posting this on a forum meant for students.
Stapel - thanks for your thoughts, all measurements are metric (mm), exterior, drawing indicates sides are 2mm and ends are 4mm. I don't think the the baffles and sender unit (float) volumes are enough to factor in (but I might), I'm only after reasonable accuracy.
I've had a few ideas about how to work this out but the brain has gone blank.
Initially I was thinking of working it out via percentages, ie the top of the tank is approx 16.27% wider than the bottom, but have so far been unable to make use of this fact.
Another thought was to rejig the volume formula W1 + W2 / 2 X H X L = Volume. But this left me with 2 unknowns.

Ishuda - the tanks are far from new and in the boat. Completely emptying the tanks, then using fuel measured in carefully in increments of 10L on a level surface is the ideal way of doing it. I have thought thought about it, but logistically it's very difficult.

Anyway, thanks again, feel free to have this thread deleted so you can continue on as intended
Cheers
Rod

 

[Ishuda]

Thanks for the replies. Sorry for posting this on a forum meant for students.
Stapel - thanks for your thoughts, all measurements are metric (mm), exterior, drawing indicates sides are 2mm and ends are 4mm. I don't think the the baffles and sender unit (float) volumes are enough to factor in (but I might), I'm only after reasonable accuracy.
I've had a few ideas about how to work this out but the brain has gone blank.
Initially I was thinking of working it out via percentages, ie the top of the tank is approx 16.27% wider than the bottom, but have so far been unable to make use of this fact.
Another thought was to rejig the volume formula W1 + W2 / 2 X H X L = Volume. But this left me with 2 unknowns.

Ishuda - the tanks are far from new and in the boat. Completely emptying the tanks, then using fuel measured in carefully in increments of 10L on a level surface is the ideal way of doing it. I have thought thought about it, but logistically it's very difficult.

Anyway, thanks again, feel free to have this thread deleted so you can continue on as intended
Cheers
Rod

O.K. - changing mm to cm since 1L = 1000 cm³
Assume tank is constant 121 cm in length, increase in width from 46.5 cm to 54 cm according to
W = 46.5 + (7.5/39) h
where h is the height and the total height of the tank is 39 cm. Then volume in the tank in liters is
V = 0.121 [46.5 + (7.5/78) h ] h
where h is the distance from the bottom in cm. This gives rise to the following table

h (cm)	V (Liter)
1.8	10
3.5	20
5.3	30
7.0	40
8.7	50
10.4	60
12.1	70
13.8	80
15.5	90
17.2	100
18.8	110
20.5	120
22.1	130
23.7	140
25.3	150
26.9	160
28.5	170
30.1	180
31.7	190
33.3	200
34.8	210
36.4	220
37.9	230
39.4	240

 

[rodfishsa]

Thanks very much Ishuda, that is great. I will use that.
I thought it interesting that each time the height changed per 10L there is one anomalous throw back to the previous amount.
Not concerned at all about that, it's only 1mm and I will adjust to get an even gradient
Thanks again for helping me out
All the best
Cheers
Rod

 

[Ishuda]

Thanks very much Ishuda, that is great. I will use that.
I thought it interesting that each time the height changed per 10L there is one anomalous throw back to the previous amount.
Not concerned at all about that, it's only 1mm and I will adjust to get an even gradient
Thanks again for helping me out
All the best
Cheers
Rod

That is the round-off getting to the numbers plus the fact that the tank is getting a bit wider even in the 'perfect model world'. Note that the increase in height starts at about 7 mm and at the end it is only about 5 mm. Since the tank probably isn't that exact inside dimensions, it won't be exactly level, and you probably won't hold the dip stick exactly perpendicular, I figured giving the measurements to within 1 mm was probably overkill anyway.