Question

# Hi Sir/Mam, following is my question: What is the length of water column that can exert 1 atm pressure?  Pls help me solve me this question.  Thnx

Solution

## Assume you made a barometer of water. A barometer is simply a large column of a liquid, where the top is sealed to form a vacuum, while the bottom is completely immersed in a trough of the same liquid. Essentially what this means is that that entire column’s weight is being balanced by the air’s pressure, without which the column would have dropped down. (For better visualization of what I explained, google Torricelli’s Barometer. He used mercury instead of water. ) Now for the math. Let the height of the column be h. we know by the pressure equation, the pressure at the bottom of the column due to the water is: p = density * gravitational acceleration * h As there is no air at the top of the column, The pressure at the bottom is solely due to water (and technically also due to the minute amount of water that evaporated inside the tube, but it doesn’t matter that much) This pressure must be balanced by the external air pressure, or the column won’t stay the way it is. thus, External atmospheric pressure = density of water * gravitational acceleration * h therefore 1atm=1000Kg/m3∗9.8m/s2∗h 1atm=101325pascals. 101325pascals=(1000∗9.8∗h)pascal/meter h=10.3393meters. So the length of water column required is:10.3393meters. I hope that answers your question.

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