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I need to try to solve, in reverse, an equation that boils down to the following:

(A+B) - (C x D) - E = X

What I need is a way to solve for "B", when X = 0

Help?

(A+B) - (C x D) - E = X

What I need is a way to solve for "B", when X = 0

Help?

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Add (C x D) + E to both sides of the equation to keep both sides balanced:

A+B = (C x D) + E

Subtract A from both sides of the equation to keep both sides balanced:

B = (C x D) + E - A

A = 10

C = 2

D = -13

E = -44

X = 0 (your requirement)

==========================

Solve for B when X = 0

B = (C x D) + E - A

B = (2* (-13)) + (-44) - 10

= -26 - 44 -10

B = -80

==========================

Plug numbers back into original to see if equations still balance:

(A+B) - (C x D) - E = X

(10 + (-80)) - (2 * (-13)) - (-44) = 0

(10 - 80) + 26 +44 = 0

-70 + 70 = 0

0 = 0 Checked

==========================

A, C, D, and E are constants that will not change. Only B and X change, but as they change, the equation holds true. If that is the case, then when X is 0, your recalculation of B should give you the correct new value for B.

You might note that if you let K = A - (C x D) - E, where K is a constant, then your equation becomes: B + K = X

Notice that as X increases or decreases by 1, then so must B increase or decrease by 1, respectively.

If you originally had a value for B and X (where X is not equal to 0), then as X goes to 0, then to keep the equation balanced, B = -K.

As long as this equation is known to be true under all of your experimental scenarios, then as X changes (and you can measure X), and as A, C, D, and E change, then you can calculate B to be (C x D) + E - A to know what B must be for the equation to hold true. (It does not matter whether D and E are constants or whether you can measure them, as long as you know what they are when X becomes 0.)

>>

OK, B is supposed to be a constant that you cannot measure directly, and you are trying to determine what the B constant is. You also note that you cannot measure X directly. There is the presumption that X must be zero when there is no flow.

Two things:

1) How can you determine the

2) Is there a chance that there is some small minimum pressure threshold that must be exceeded to have a flow? That is, if the pressure on one side of the filter is very small (but greater than zero), then that pressure is not enough to get through the resistance of the filter.

Could you please label each of the terms?

At zero flow, I'd expect the MediaThickness and FilterHeadLoss both to drop out of the equation. Downstream pressure ought to equal the water level.

And at constant flow under clean conditions, there ought to be a pressure drop equal to a factor (greater than 1) times the media thickness. The term you call MediaThickness would equal that factor less one under clean conditions. And under fouled conditions, it would have one flow resistance for the fouled portion of the filter, and the original flow resistance for the unfouled bottom portion of the filter media.

The pdf file I linked to confirms this with its discussion of how to solve problem b (in the pdf).

The formula you are trying to plug into is only relevant when there is flow through the filter.

In other words, even if you could solve for B when x is zero, the answer would be a meaningless artifact of test conditions.

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