Question

The pressure exerted by a column of liquid is equal to the product of the height of the column times the gravitational constant times the density of the liquid, P= ghd. How high a column of methanol ( d=0.79g/ml) would be supported by a pressure that supports a 713mm column of mercury ( d= 13.6g/ml)?

Answer 1

The column of methanol is = 12.27 m high

Step-by-step explanation:

The pressure of mercury (p) = ghd,................... equation 1

Where g = acceleration due to gravity, h= height, d = density.

d = 13.6 g/ml convert to kg/m³ = 13.6 g/ml(1000 (kg/m³)/(g/ml))

d =13600 kg/m³., h= 713mm = 713/1000 = 0.713 m., g= 9.80 m/s²

Substituting these values into equation 1,

P = 13600 × 0.713 × 9.8 = 95028.64 N/m².

If the pressure of the mercury supports the pressure exerted by the methanol

∴ pressure that supports the mercury = pressure of the methanol

p = ghd

making h the subject of formula,

h = p/gd ........................... equation 2

Where p = 95028.64 N/m², g = 9.8 m/s², d = 0.79 g/ml = (0.79 × 1000) kg/m³

d = 790 kg/m³.

Substituting these values into equation 2

h = 95028.64/(9.8×790)

h = 95028.64/7742

h = 12.27 m.

The column of methanol is = 12.27 m high