I'm building a press for cider. I'm going to be using a 24" x 24" press board. I'm looking to deliver 40 psi to the cider. How can I determine the amount of weight required, in tons? What sort of equation would I use?
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2$\begingroup$ You can try: p=F/A, F= m*g $\endgroup$– Jaroslav KotowskiApr 22, 2015 at 6:41
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$\begingroup$ @JaroslavKotowski That looks very helpful. Could you give me a small example? I'm having just a little trouble fully comprehending. :) $\endgroup$– David CusterApr 22, 2015 at 6:44
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2$\begingroup$ 24" = 0.6096m; Area = 0.3716m^2; 40psi = 275 790 kg/m/s^2; g = 9.81m/s^2; F = Area*Pressure = 102.486kgm/s^2; m = F/g = 10447kg $\endgroup$– rul30Apr 22, 2015 at 6:57
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2$\begingroup$ @rul30 OP gave his question in imperial units and specifically asked for answer in tons. While there are multiple tons, given that he already used imperial, I would assume he's looking for short tons, or at the very least, not metric tons. Feel free to give an answer in multiple unit systems, but use at least the system that OP requests. $\endgroup$– Trevor ArchibaldApr 22, 2015 at 16:49
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2$\begingroup$ On a general note, though this question may seem simple to those of us for whom the basic pressure equation is as reflexive as 2+2, the answers should still be posted as answers, not comments. Comments are more likely to end up hidden if a long chain starts, and can be deleted with much less care. A full answer gives you more opportunity to explain, and also gives you an opportunity to earn some delicious, juicy rep. $\endgroup$– Trevor ArchibaldApr 22, 2015 at 16:52
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2 Answers
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The obvious place to start is "what does psi mean?" It's an abbreviation for "pounds per square inch".
If we have a 24" x 24" board, then we have
$$24~in\times24~in=576~in²$$
To get 40psi, i.e. 40 pounds for each square inch, we would need
$$40~\frac{lbs}{in²}*576~in² = 23040 ~lbs$$.
You've asked for an answer in tons, so we need to convert 23040 pounds to tons. Assuming you're using the US short ton, there are 2000 pounds in a ton. So we need
$$23040 ~lbs/2000 ~\frac{lbs}{ton} = 11.52~US~tons$$
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The calculation you made in your comment is correct.
$11.52 \:\mathrm{US} \:\mathrm{tons} = 23,040 \:\mathrm{lb_f}$
$\dfrac{23,040 \:\mathrm{lb_f}}{24″ \times 24″} = 40 \:\mathrm{psi}$
