Mixing
Volume calculation with varying thickness
$begingroup$
I have rectangular slabs which I printed, the thickness varies from 9.8mm to 10.08 on one side and width varies from 10-10.6 mm , the height is 20mm. How can I calculate the actual volume? Is there any mathematical procedure to introduce these varying thickness and get a good estimate of the volume? What is the best method to average this varying thicknesses? How can I measure the actual volume experimentally, if its not too difficult? Need precise volume measurements. Thanks for the help in advance.
geometry volume
asked Jan 26 at 1:51
veda narayana veda narayana
11
$endgroup$
add a comment |
$begingroup$
I have rectangular slabs which I printed, the thickness varies from 9.8mm to 10.08 on one side and width varies from 10-10.6 mm , the height is 20mm. How can I calculate the actual volume? Is there any mathematical procedure to introduce these varying thickness and get a good estimate of the volume? What is the best method to average this varying thicknesses? How can I measure the actual volume experimentally, if its not too difficult? Need precise volume measurements. Thanks for the help in advance.
geometry volume
asked Jan 26 at 1:51
veda narayana veda narayana
11
$endgroup$
$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47
add a comment |
$begingroup$
I have rectangular slabs which I printed, the thickness varies from 9.8mm to 10.08 on one side and width varies from 10-10.6 mm , the height is 20mm. How can I calculate the actual volume? Is there any mathematical procedure to introduce these varying thickness and get a good estimate of the volume? What is the best method to average this varying thicknesses? How can I measure the actual volume experimentally, if its not too difficult? Need precise volume measurements. Thanks for the help in advance.
geometry volume
asked Jan 26 at 1:51
veda narayana veda narayana
11
$endgroup$
I have rectangular slabs which I printed, the thickness varies from 9.8mm to 10.08 on one side and width varies from 10-10.6 mm , the height is 20mm. How can I calculate the actual volume? Is there any mathematical procedure to introduce these varying thickness and get a good estimate of the volume? What is the best method to average this varying thicknesses? How can I measure the actual volume experimentally, if its not too difficult? Need precise volume measurements. Thanks for the help in advance.
geometry volume
geometry volume
asked Jan 26 at 1:51
veda narayana veda narayana
11
asked Jan 26 at 1:51
veda narayana veda narayana
11
edited Jan 26 at 5:29
veda narayana
asked Jan 26 at 1:51
veda narayana veda narayana
11
asked Jan 26 at 1:51
veda narayana veda narayana
11
asked Jan 26 at 1:51
veda narayana veda narayana
11
11
$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47
add a comment |
$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47
$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
One approach is to measure the dimensions on opposite sides of the block and average them. This will be correct if the dimensions vary linearly. If the piece is thick in the middle and thin on the edges, not so much.
Another approach is to weigh the blocks. You can do that very accurately with a good scale. If the density is known you have to volume. You could make some blocks that you machine to good parallelepipeds so you can measure them well, weigh them, and use that density. If you do a few you can justify how repeatable the density is.
Another approach is water (or other liquid) displacement. Start with a known volume of water, submerge the object, and measure the total volume. Volumes are harder to measure accurately, so this may not be so good for you.
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
$endgroup$
add a comment |
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1 Answer
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$begingroup$
One approach is to measure the dimensions on opposite sides of the block and average them. This will be correct if the dimensions vary linearly. If the piece is thick in the middle and thin on the edges, not so much.
Another approach is to weigh the blocks. You can do that very accurately with a good scale. If the density is known you have to volume. You could make some blocks that you machine to good parallelepipeds so you can measure them well, weigh them, and use that density. If you do a few you can justify how repeatable the density is.
Another approach is water (or other liquid) displacement. Start with a known volume of water, submerge the object, and measure the total volume. Volumes are harder to measure accurately, so this may not be so good for you.
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
$endgroup$
add a comment |
$begingroup$
One approach is to measure the dimensions on opposite sides of the block and average them. This will be correct if the dimensions vary linearly. If the piece is thick in the middle and thin on the edges, not so much.
Another approach is to weigh the blocks. You can do that very accurately with a good scale. If the density is known you have to volume. You could make some blocks that you machine to good parallelepipeds so you can measure them well, weigh them, and use that density. If you do a few you can justify how repeatable the density is.
Another approach is water (or other liquid) displacement. Start with a known volume of water, submerge the object, and measure the total volume. Volumes are harder to measure accurately, so this may not be so good for you.
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
$endgroup$
add a comment |
$begingroup$
One approach is to measure the dimensions on opposite sides of the block and average them. This will be correct if the dimensions vary linearly. If the piece is thick in the middle and thin on the edges, not so much.
Another approach is to weigh the blocks. You can do that very accurately with a good scale. If the density is known you have to volume. You could make some blocks that you machine to good parallelepipeds so you can measure them well, weigh them, and use that density. If you do a few you can justify how repeatable the density is.
Another approach is water (or other liquid) displacement. Start with a known volume of water, submerge the object, and measure the total volume. Volumes are harder to measure accurately, so this may not be so good for you.
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
$endgroup$
One approach is to measure the dimensions on opposite sides of the block and average them. This will be correct if the dimensions vary linearly. If the piece is thick in the middle and thin on the edges, not so much.
Another approach is to weigh the blocks. You can do that very accurately with a good scale. If the density is known you have to volume. You could make some blocks that you machine to good parallelepipeds so you can measure them well, weigh them, and use that density. If you do a few you can justify how repeatable the density is.
Another approach is water (or other liquid) displacement. Start with a known volume of water, submerge the object, and measure the total volume. Volumes are harder to measure accurately, so this may not be so good for you.
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
answered Jan 26 at 5:50
Ross MillikanRoss Millikan
300k24200374
300k24200374
add a comment |
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$begingroup$
My apologies. Didn't write the question properly. I have edited it,both the thickness and the width are varying.
$endgroup$
– veda narayana
Jan 26 at 5:30
$begingroup$
Thanks for the update. I'll repeat my suggestion of the principle of displacement, although this actually gives more information than just the physical volume. Mathematically the slowly(?) varying thickness $T$ and width $W$ can be considered functions of the height $0le x le 20$, Different slabs would seem to have different volumes, but perhaps one can model the distribution of volumes from information about "random variable" $T$ and $W$ and their covariance.
$endgroup$
– hardmath
Jan 26 at 5:47