What is the volume of a cylindrical wine barrel with a bung hole?

If t is meant to be r/h, then your formula isn't quite right.In summary, a wine barrel has a bung hole in the middle of its side, and a bung rod can be inserted to determine the volume of wine inside. Assuming the barrel is cylindrical, with the bung hole centered along the length and a distance of d from the corner, and with a ratio of length to diameter represented by t, the volume of the barrel can be shown as V=2(pi)d^3t(4+t^2)^(-3/2). However, there may be missing information or a mistake in the equation, as t's representation is not specified.
  • #1
blakjack
1
0

Homework Statement



A wine barrel has a hole in the middle of its side called a bung hole. To determine the volume of the wine in the barrel, a bung rod is inserted in the hole until it hits the lower seam.
You should make the following assumptions:
-The barrel is cylindrical
-The bung hole is centered along the length of the barrel
-The distance from the bung hole to the corner is d
-The ratio of the length to the diameter of the barrel is t.
Answer the following questions:
You should show that the volume of the cylindrical barrel is V=2(pi)d^3t(4+t^2)^(-3/2)

I don't know how to arrive at the fact that the volume would be what is shown.


Homework Equations


V = pi r^2 h

The Attempt at a Solution


I set the two equations next to each other and tried to see what canceled out which was pi.

So r ^ 2 h = 2(d^3t)(4+t^2)^(-3/2)

Then I got stuck and help would be greatly appreciated.
 
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  • #2
I think you're missing something, since there's no indication anywhere of what [itex]t[/itex] represents.
 

What is Kepler's wine barrel volume formula?

Kepler's wine barrel volume formula is V = πr2h, where V is the volume, r is the radius, and h is the height of the barrel.

How accurate is Kepler's wine barrel volume formula?

Kepler's wine barrel volume formula is highly accurate for traditional wine barrels with a cylindrical shape. However, it may not be as accurate for irregularly shaped or non-cylindrical barrels.

Can Kepler's wine barrel volume formula be used for any type of barrel?

No, Kepler's wine barrel volume formula is specifically designed for traditional cylindrical wine barrels. It may not accurately calculate the volume of other types of barrels.

What units are used in Kepler's wine barrel volume formula?

The units used in Kepler's wine barrel volume formula can vary, but typically the radius and height are measured in feet or meters, and the volume is given in cubic feet or cubic meters.

Is Kepler's wine barrel volume formula the only way to calculate the volume of a wine barrel?

No, there are other methods for calculating the volume of a wine barrel, such as using water displacement or measuring the internal dimensions and calculating the volume using geometry formulas. However, Kepler's formula is commonly used and considered to be quite accurate for traditional wine barrels.

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