| The Hydrostatic
Paradox has several forms. The Liquid
Level Vase has several liquid-filled tubes connected to the same reservoir,
and the liquid rises to the same level in all of the tubes.
The actual pressure at the bottom of the vase can be measured with the apparatus at the right and below. These are unequal-arm balances, in which the downward force on the left-hand side given by the product of the pressure at the bottom of the vessel of water and the cross-section of the vessel at this point. The force is actually exerted on a circular metal disk which presses against the bottom of the vessel. A group of weights is hung from the right-hand side of the balance; they are initially large enough to keep the disk in place. Weights are then slowly removed until the system becomes unbalanced and water runs out of the bottom of the vessel. Proving the truth of the paradox requires the use of vessels of several shapes, but always with the same bottom cross-section area and filled to the same depth. All of them will start to leak at the same value of the balancing weight.
| The apparatus above is in the Collection of Historical
Instruments at Harvard University. It was made by Max Kohl ca. 1900.
At the left is a Pascal's Vase at Hampden-Sydney College made by C. Gerhardt of Bonn.
Central Scientific Company used to make a similar apparatus with a mechanical pressure sensor attached to a dial. I use one, made perhaps seventy years ago, in a demonstration every year for the introductory students.
Other versions of Pascal's vases use an external mechanism for providing the upward force to keep the vase from leaking. The Wittenberg apparatus was almost certainly made by Queen of Philadelphia and cost $15.00 in the 1881 catalogue. A brass disk was pressed tightly against the bottom of the vase by a string reaching upward and attached to one arm of a balance. The Denison apparatus was bought from Central Scientific Company on August 29, 1905.
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