## [SOLVED] Calculation question (probably simple, but I'm bad at it)

Pjotr
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### [SOLVED] Calculation question (probably simple, but I'm bad at it)

I have a calculation question concerning the refreshing of the power steering fluid in my car. It should probably be simple for me, but I'm pretty bad at arithmetic.
So I'd really appreciate it if you would check my calculation:

The total amount of power steering fluid in my car, is 700 cc. I'm using a turkey baster, with which I can extract a maximum of 200 CC from the power steering fluid reservoir. That's about 28 % (well, a bit more, but round figures suffice).

I want to repeat this several times, using the car in between so the new fluid gets mixed well with the old fluid, until the percentage of old fluid has diminished sufficiently.

Now my calculation:

I've bought a can of 1.000 cc new fluid (ATF Dexron III). This allows for five consecutive refreshings of 200 cc each. I've just completed the second refreshing.

- The first refreshing has reduced the old fluid by 28 % (200 : 700), leaving 72 % of old fluid in the resulting mix.
- The second refreshing has reduced the old fluid by 20 % (72 x 0,28), leaving 52 % of old fluid in the resulting mix.
- The third refreshing will reduce the old fluid by 14 % (52 x 0,28), leaving 38 % of old fluid in the resulting mix.
- The fourth refreshing will reduce the old fluid by 10 % (38 x 0,28), leaving 28 % of old fluid in the resulting mix.
- The fifth and final refreshing will reduce the old fluid by 8 % (28 x 0,28), leaving an acceptable 20 % of old fluid in the resulting mix.

Now, is this calculation correct of is it bollocks?
Last edited by Pjotr on Tue Sep 01, 2020 2:06 pm, edited 1 time in total.
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DAMIEN1307
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### Re: Calculation question (probably simple, but I'm bad at it)

Hi pjotr,

I dont pretend to know the maths calculations your trying to use, but here in the U.S., we would simply go to a motor vehicle service center and ask for a "power steering flush" which would replace ALL of the used brownish, yucky, burnt fluid with new ATF.

Does this service exist in the Nederlands ?...its usually not very expensive and it would give you the peace of mind that with the fluid replacement being total, you could therefore extend the life of your power steering unit...DAMIEN
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Pjotr
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### Re: Calculation question (probably simple, but I'm bad at it)

DAMIEN1307 wrote:
Tue Sep 01, 2020 1:26 pm
Hi pjotr,

I dont pretend to know the maths calculations your trying to use, but here in the U.S., we would simply go to a motor vehicle service center and ask for a "power steering flush" which would replace ALL of the used brownish, yucky, burnt fluid with new ATF.

Does this service exist in the Nederlands ?...its usually not very expensive and it would give you the peace of mind that with the fluid replacement being total, you could therefore extend the life of your power steering unit...DAMIEN
That's the easy way out, also here in The Netherlands, but I like to do some car maintenance myself.
A net result of 20 % old fluid in the mix (if my calculation is correct!) is fine with me. Considering that replacing the power steering fluid is even deemed wholly unnecessary by Toyota, regardless of age and mileage (I have a Yaris).
Last edited by Pjotr on Tue Sep 01, 2020 1:30 pm, edited 1 time in total.
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Welcome
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### Re: Calculation question (probably simple, but I'm bad at it)

Looks good to me. I used a slightly different method on a spreadsheet, and it calculates 18.6% on the fifth replacement.

But, all this assumes a complete and thorough mixture, including all hoses and cylinders.

Why do you want to replace the steering fluid?
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Pjotr
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### Re: Calculation question (probably simple, but I'm bad at it)

Welcome wrote:
Tue Sep 01, 2020 1:29 pm
Why do you want to replace the steering fluid?
The car is 19 years old and has run almost 250.000 kilometres. Can't hurt to refresh the fluids a bit, even if it's not on the official maintenance schedule (like in this case)....
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DAMIEN1307
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### Re: Calculation question (probably simple, but I'm bad at it)

On toyotas i have owned, i have done a do it yourself type of flush also using a turkey baster.

What i did was to first have the vehicle running and had my son slowly steer the wheel left to right repeatedly going stop to stop while i would extract a baster full of fluid, and then have another baster full of new fluid and add what i just took out and kept repeating the process until i had clean fluid throughout the system...it works well...DAMIEN

HINT...The slow steering back and forth ensures that you will bleed any air out of the system while "basting" the turkey...lol., as well as insuring the new fluid has access to the entire PS system while expelling the old fluid.
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senjoz
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### Re: Calculation question (probably simple, but I'm bad at it)

My result of quick calculation is: after five refreshments you would have 18.6 % of old fluid.

Regards, Jože
Last edited by senjoz on Tue Sep 01, 2020 2:07 pm, edited 1 time in total.
Pjotr
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

Thanks Welcome and senjoz! With two independent confirmations, I think we can consider this as solved.
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Pjotr
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### Re: Calculation question (probably simple, but I'm bad at it)

DAMIEN1307 wrote:
Tue Sep 01, 2020 1:37 pm
On toyotas i have owned, i have done a do it yourself type of flush also using a turkey baster.

What i did was to first have the vehicle running and had my son slowly steer the wheel left to right repeatedly going stop to stop while i would extract a baster full of fluid, and then have another baster full of new fluid and add what i just took out and kept repeating the process until i had clean fluid throughout the system...it works well...DAMIEN

HINT...The slow steering back and forth ensures that you will bleed any air out of the system while "basting" the turkey...lol., as well as insuring the new fluid has access to the entire PS system while expelling the old fluid.
I have considered such a method, but it's straining for the wheels (unless you jack up both front wheels). And the additional advantage of keeping the steering wheel unturned while refreshing the fluid, is that you can be pretty sure that no air gets sucked in.
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### Re: Calculation question (probably simple, but I'm bad at it)

I'm certainly no expert on this, but I would suspect the mix (especially the first, and probably the second and third) would degrade the new fluid as much as it's refreshing the old fluid. Even ending at 20% old, you may have a mix that only has half or less the life expectancy.

Keep in mind, I say this as someone that uses those band-aid fluid leak additives. I'd probably do the same as you if I were to attempt preventative maintenance.

And again, my suspicion may be full of manure.
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### Re: Calculation question (probably simple, but I'm bad at it)

MrEen wrote:
Tue Sep 01, 2020 2:14 pm
I'm certainly no expert on this, but I would suspect the mix (especially the first, and probably the second and third) would degrade the new fluid as much as it's refreshing the old fluid. Even ending at 20% old, you may have a mix that only has half or less the life expectancy.
Well, I've heard something like that before, but I can't really believe that.

Note that with an ordinary engine oil flush in the official garage, even if they drain it, some old oil always remains in the engine. They can't remove all of it by means of the drain plug. Perhaps as much as 5 - 10 % old oil is still in the engine then, which mixes with the new replacement oil that's being added.

Now that isn't considered to be a problem at all... So how could 20 % old fluid have such a big negative effect?
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### Re: Calculation question (probably simple, but I'm bad at it)

Pjotr wrote:
Tue Sep 01, 2020 2:23 pm
So how could 20 % old fluid have such a big negative effect?
Because it's not 20% the first few times of replacement, it's 72% the first time mixing with only 28% new fluid.

And I stress again, I'm not talking from any sort of experience or knowledge, but here's an example of my thinking:

Do the same with a litre of sour milk. Replace with fresh milk using the same percentages. Is the final product drinkable? Even if it is, will it remain drinkable half as long as new milk?

And I know, totally different things here much like apples and oranges. I think the viscosity and impurities are the big factor here. If I could afford it, I'd certainly prefer a flush and fill.
cliffcoggin
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

The problem with repeated partial dilution is that you can never entirely get rid of all the old fluid. A better approach is to flush the hydraulic system from the master cylinder to each slave cylinder in turn, a process known here as "bleeding the brakes". An assistant to pump the pedal and top up the cylinder is needed, plus a suitable spanner that fits the brake nipples. Not only does this method change all the fluid, it also expels any air.
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

cliffcoggin wrote:
Tue Sep 01, 2020 2:51 pm
The problem with repeated partial dilution is that you can never entirely get rid of all the old fluid.
True, but it's purely preventative maintenance to begin with. One might even call it extracurricular, because changing the power steering fluid doesn't even feature in Toyota's official maintenance schedule.

Furthermore, I've also been doing engine oil changes and automatic gearbox fluid changes, like this for years. Those turkey basters are useful stuff. This is what I use: https://pelaproducts.eu/pela-400/

Saved lots of money this way. And both my car and my wife's car (also a Toyota Yaris, also 250.000 kilometres) keep happily purring along, without any problems whatsoever....

With this kind of oil and fluid maintenance, I have no doubt that both cars will be able to run 500.000 kilometres or more. For a song, because I buy premium brand synthetic engine oil (Valvoline) for a ridiculously low price at a discounter.
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slipstick
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

Too late to be useful, but I couldn't resist (see my user name)

This is so easy with a slide rule.
* move the runner to place the hairline over .72 on the inverse LL2 scale
* move the slide to bring 5 on the CI scale under the hairline
* move the runner to place the hairline over the left index of the C scale and under the hairline on the inverse LL3 scale read 0.1935 (approx.), so 19.4 % old fluid remains

My calculator shows 0.72^5 = 0.19349....
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MrEen
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

slipstick wrote:
Tue Sep 01, 2020 3:32 pm
Too late to be useful, but I couldn't resist (see my user name)

This is so easy with a slide rule.
* move the runner to place the hairline over .72 on the inverse LL2 scale
* move the slide to bring 5 on the CI scale under the hairline
* move the runner to place the hairline over the left index of the C scale and under the hairline on the inverse LL3 scale read 0.1935 (approx.), so 19.4 % old fluid remains

My calculator shows 0.72^5 = 0.19349....
Yeah, but I bet you can't change the theme on that.
senjoz
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

slipstick wrote:
Tue Sep 01, 2020 3:32 pm
My calculator shows 0.72^5 = 0.19349....
Maybe I am to exact, I believe it is 0.714^5 = 0.186

Regards, Jože
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

senjoz wrote:
Tue Sep 01, 2020 3:50 pm
Maybe I am to exact, I believe it is 0.714^5 = 0.186
Approximately.

The exact answer is that you have `(5/7)^n` original fluid left where n is the number of times you did the procedure. Each time you remove 200/700 you have remaining 5/7.

This reminds me that I once read and saw proof that we each have passed through our bodies molecules of water that passed through the body of Columbus. Take the amount of water passed thought his body in his lifetime, dilute all those molecules evenly in the planet and the chances that some have passed your body are close to 100%.

You have not only peed water molecules that Columbus himself peed... you have drunk water molecules that Columbus himself peed.
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slipstick
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

senjoz wrote:
Tue Sep 01, 2020 3:50 pm
slipstick wrote:
Tue Sep 01, 2020 3:32 pm
My calculator shows 0.72^5 = 0.19349....
Maybe I am to exact, I believe it is 0.714^5 = 0.186

Regards, Jože
My slide rule will do that, too.
I get approx. 0.1858 on the sliderule (last digit interpolated as well as my eyes will allow). Calculator says 0.18556...... Close enough for "government work".
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GS3
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### Re: [SOLVED] Calculation question (probably simple, but I'm bad at it)

(5/7)^5 = 3125 / 16807 = 0.18593443.... approximately
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