A pressure that will support a column of Hg to a height of 256 mm would support a column of water to what height? The density of mercury is 13.6 g/cm3; the density of water is 1.00 g/cm3.

The height of water in the column = 348.14 cm

Explanation:

Pressure:This is defined as the ratio of the force acting normally (perpendicular) to the area of surface in contact. The S. I unit of pressure is N/m²

p = Dgh ... Equation 1

Where p = pressure, D = density, g = acceleration due to gravity, h = height.

From the question, the same pressure will support the column of mercury and water.

p₁ = p₂

Where p₁ = pressure of mercury, p₂ = pressure of water

D₁gh₁ = D₂gh₂ ... Equation 2

making h₂ the subject of equation 2

h₂ = D₁gh/D₂g ... Equation 3

Where D₁ and D₂ = Density of mercury and water respectively, h₁ and h₂ = height of mercury and water respectively

Given: D₁ = 13.6 g/cm³, D₂ = 1.00 g/cm³, h₁ = 256 mm = 25.6 cm.

Constant: g = 9.8 m/s²

Substituting these values into Equation 3,

h₂ = (13.6*9.8*25.6) / 1*9.8

h₂ = 348.14 cm

The height of water in the column = 348.14 cm