Calculation Needed 3

[dik]

I'm trying to calculate the volume of a tank with a base that slopes in two directions. The four corners have different lengths. I can solve the problem with sorting the four different lengths.

Does anyone know of a formula that can calculate the volume just using the four measurements. They may or may not be equal and one or more can be zero.

Alternatively, does anyone know how to sort four rows of data without using an if command? I want to use the four values, but sort them by reference without using the Data menu...

Dik

 

[RWF7437]

Unless your tank volume needs to be VERY accurate use the average end area method. If the tank shape is a regular solid an exact method may be available. I can't see why it would be either necessary or desirable to "sort" the known lengths.

good luck

 

[dik]

RWF... with the data sorted, it's possible to calculate the volume from the rectangle using the least height, the two wedges from the next two sorted height and the triangular tetrahedron from the greatest height... it not the precision, but if you have to make the calculation... the accuracy is free once you have the method... There should be some method of sorting the data without having to use Data menu...

Dik

 

[RWF7437]

Guess I don't understand your question. How can a "corner" have a length? Isn't a corner a point? What kind of tank is this ? What good is "free" accuracy if you don't need it ? What's wrong with using the sort/data menu or commands ? Are you using Excel or some other spreadsheet? Can you simply fill the "tank" with water and measure the amount needed to fill ? If you have 4 measurements, what does your statement; " They may or may not be equal and one or more can be zero." mean ? Try restating your question or posting it on other fora. Maybe someone can understand what you are trying to do.

good luck

 

[dik]

sorry... the depth of the tank at each of the four corners

 

[RWF7437]

Dik,

One of the maddening things about these fora is the difficulty in trying to convey questions clearly, using only words. Probably one sketch would make your question a lot clearer.

Nevertheless, it sounds like you have a rectangular tank (?) and know the plan dimensions of the rectangle (?). You also know the depth of the tank at each of its four (90°?)corners. You say the tank bottom slopes in two directions (?) but you don't say in what direction these slopes are or whether or not they are uniform. It sounds like you don't have enough information to calculate the volume, or you haven't told us everything you know.

If you have more information, please share it. If not, no spreadsheet can provide it for you. Also, it would help a lot if you answer the questions in the previous post.

good luck

 

[dik]

I think the problem was formulated in the first sentence I posted...

I'm trying to calculate the volume of a tank with a base that slopes in two directions.

Dik

 

[RWF7437]

But not clearly or completely.

 

[IFRs]

Are you saying you have a square tank whose bottom slopes uniformly from a point off center in a random direction? Is the bottom slope up or down? Do you essentially you have a pyramid whose base is square but whose crown is off center? Is it a pyramid whose base is comprised of four unequal lengths? And somehow you know the diagonal lengths and they are all different? Do you know the lengths of the sides? Is the tank square, rectangular, rhombus, etc? Do you know the height of the crown?

 

[GregLocock]

Is the base of the tank a flat, sloping, plane? Is the tank rectangular in plan view? If so the average of the four depths is the right answer, at a guess.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[yakpol]

Four sides don't completely describe a plane shape, not like in the case of a triangle.

 

[GregLocock]

?

It is an overcosntrained solution. 3 depths define the plane, the fourth is along for the ride.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MintJulep]

The path to the answer starts here:

http://www.ac-noumea.nc/maths/amc/polyhedr/tetra_.htm

 

[yakpol]

dik,
If I understand it right, the shape of the tank is a truncated pyramid, then

Volume = h[A+a+sqrt(Aa)]/3

, where A and a are areas of bottom and top bases.
Answering your second question about sorting without using data commands: try function LARGE in combination with MATCH or LOOKUP for associated columns.

yakpol

 

[NKT]

Dik:

One way to create a sorted list of input data is with the "SMALL" command. The input format is "=SMALL(array,k)" where "array" is the range of data you are trying to sort, and the function gives the k'th smallest value. You would have to input this formula once for each cell in the array, with k=1 to k=4 in the situation you describe.

NKT

 

[dik]

NKT... thanks, did the trick. I just plugged this in in lieu of the sorted variables and it works... even for zero values for depths... I didn't know about the SMALL command and if all values are equal it still returns the correct value... thanks, I wish I could give you two stars!

Dik