# A question on Hydraulics from a 19th century book

The following passage is from a 19th century physics text.

"Take a strong glass tube about three feet in length, and tie over one end a piece of well-soaked bladder. "When thoroughly dry, fill the tube with mercury, and invert it in a cup of the same liquid. The mercury will sink to a height of about 30 inches. If the area of the tube be one inch, this amount of the metal will weigh about 15 Ibs. The weight of the column of mercury is equal to the downward pressure on each square inch of the surface of the mercury in the cup. Hence we conclude that the pressure of the atmosphere is 15 Ibs. per square inch, and will balance a column of mercury 30 inches high. As water is 13 1/2 times lighter than mercury, it is evident that the same pressure would balance a column of that liquid 13 1/2 times higher, or 33 3/4 feet. On account of the unwieldy length of the tube required to exhibit the column of water, it is not easy to verify this last statement. It may, however, be prettily illustrated in the following manner. Pour on the mercury in the cup (Fig. 102) a little water colored with red ink. Now raise the end of the tube carefully above the surface of the metal, but not above that of the water which will immediately rise in the tube, the mercury passing down in beautifully beaded globules. The mercurial column was only 30 inches high, while the water will entirely fill the tube. Finish the experiment by puncturing the bladder with a pin, when the water will instantly fall to the cup below."

It can be found here https://archive.org/details/fourteenweeksinn00steerich/page/138/mode/2up

I confess I do not entirely understand this passage. In particular why will puncturing the bladder cause the water to flow out ? What is the function of the bladder ? Also what fills the remainder of the tube in the column of mercury ? Is it a vacuum ?

Thanks for any insight in the further explanation of this passage.

Take a strong glass tube about three feet in length, and tie over one end a piece of well-soaked bladder. When thoroughly dry, . . . .
The dry bladder provides a stiff and air-tight seal at one end of the tube.
Two boys with a bladder is a painting which shows a pig's bladder being blown up by a boy.

. . . . fill the tube with mercury [with the bladder seal at the bottom], and invert it in a cup of the same liquid [with the bladder seal at the top]. The mercury will sink to a height of about 30 inches.
A mercury barometer has been made with a (Torricellian) vacuum above the mercury.

Pour on the mercury in the cup . . . . a little water coloured with red ink. Now raise the end of the tube carefully above the surface of the metal, but not above that of the water, the mercury passing down in beautifully beaded globules
So now you have water below the column of mercury in the tube and as water is less dense than mercury it will rise up the tube displacing the mercury in the tube.

The mercurial column was only 30 inches high, while the water will entirely fill the tube.
This is because a barometer with water will have a vertical water column height $$33 \frac 13$$ feet $$[\approx \,10\,\rm m]$$ and as the tube used in this experiment is less than this length the water will rise right to the top of the tube.

Finish the experiment by puncturing the bladder with a pin, when the water will instantly fall to the cup below.
With a hole in the bladder the pressure at the top of the column of water now becomes atmospheric so the water in the tube drops until it is the same level as the surface of the water outside the tube.

The book was first published in $$1878$$ at a time when "Health & Safety" was of little concern.

• Thanks for this answer, I am still trying to understand the last comment, the bladder is permeable, so what does it matter if it is punctured ? Jun 26, 2022 at 22:49
• It is permeable to water and mercury. That is in the experiment. Jun 26, 2022 at 23:06
• oh, you mean there is no transfer and that the bladder expands ? But it says the water will rise in the tube and the mercury comes out in globules, this implies that it is permeable. Jun 26, 2022 at 23:15
• oh, ok, the bladder is at the top. I thought it was immersed in the fluid. So when the mercury first descends, it draws the bladder in. But when the water ascends the resultant atmospheric pressure is countered by the elasticity of the bladder. Then of course puncturing, the bladder will equalize the air pressure and normal equilibrium results. Jun 26, 2022 at 23:25