Question

The atmosphere pressure can support mercury in a tube, which the upper end is closed, up to 0.76 meter. If the mercury is replaced by pure water in this case, what is the maximum height the atmosphere pressure can support the water in such kind a tube? (The density of mercury is about 13.6 times larger than that of water).

Answer 1

Maximum height the atmosphere pressure can support the

water=10.336 m

Step-by-step explanation:

We know that ,

`Pressure = h\cdot\rho\cdot g`

Case 1 - Mercury in the tube

`Density\ of\ mercury =\rho_1\\and\ height\ attained\ for\ mercury\ column = h_1`

Case 2 - Water in the tube

`Density\ of\ water =\rho_2\\and\ height\ attained\ for\ water\ column = h_2`

Since atmospheric pressure is same

.
`P=h_1\cdot\rho_1\cdot g = h_2\cdot\rho_2\cdot g`

or,
`h_2=(h_1\rho_1)/(\rho_2)`

`Given\ h_1= 0.76\ m,\rho_1=13.6\cdot\rho_2`

∴
`h_2=0.76\cdot13.6=10.336\ m`

Hence height of the water column =10.336 m