Converting between dimensions?

Question

I just posted a question and got feedback that it is not possible to convert meters cubed to meters. I am a chemical engineering major and am working a problem. I am told benzene weighs 0.879 g/cm^3 and the tank it is filling is 2 meters in diameter and 4 meters long. I am told to derive a formula for the weight of benzene as a function of h, the height of the tank. I was thinking convert to meters then multiply by 4. Since I have been told I cannot convert different dimensions, do you have any suggestions as to how to tackle this problem.

Answer 1

You can convert from cubic centimeters to cubic meters - the multiplyer is in the back of one of your textbooks.

Getting the volume of the tank might be tricky if it's not a simple cylinder. In all the years I've been doing tanks, pressure vessels, piping and liquid level gauges for industry, most of the tanks I've seen in that size range have elliptical heads. It's essentially 'dome-shaped' with an elliptical cross section.

There is a way to get the volume of the heads but I don't have the formulae with me here at home. Many of the manufacturers of the heads will have data that show you how much volume in each head size. It may come in the form of a chart for each "h" depending on whether it's horizontal or vertical.

However, if it's part of a school assignment, then the problem probably allows you to assume a simple cylinder. The next question you should ask is whether that's 2 meters INSIDE diameter or OUTSIDE dia. The wall thickness can be a lot of cubic centimeters, and throw off your calculations.

So you start with the inside dia and figure the cc volume of 1 centimeter of depth. From there, "h" is just an accumulation of that volume for "1 centimeter depth" mulitiplied by the number of centimeters of "h". But that's if it's a vertical cylinder.

If it's a horizontal cylinder then you need to spend more time playing with the geometry. In effect, it's a "chord" of the cylinder. Start with the inside radius and subtract one centimeter - that's your first chord. Then you need to do the same for subtracting two centimeters. etc etc etc.

Remember, working with smaller increments will give you more accurate answers.

Answer 2

You cannot convert volume to distance - they're two different things.

The point is though - your tank has a volume - 2m dia x 4 long. You can easily work out the volume using pi x r squared (area of base), and multiply by the height.

Then use your volumetric weight of the benzene to work out the weight of the benzene in that volume.

I could do it for you, but what I think you really needed is some guidance on what to do.

Answer 3

You would be writing an equation for
volume, (Cubic Meters), x benzene density,
with height,(the last linear dimension),
as the variable.
You would still be working with a volume,
which is a function of three linear measures.

Answer 4

You're chemical engineering and you don't know that you CAN'T convert from length to volume?????????


whew

Answer 5

.879*100000 *pi* H should do it in this case