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7 June, 06:43

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.

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  1. 7 June, 09:45
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    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
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