Question

Mercury is added to a cylindrical container to a depth d and then the rest of the cylinder is filled with water. If the cylinder is 0.8 m tall and the absolute (or total) pressure at the bottom is 1.1 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36 104 kg/m3, and the ambient atmospheric pressure to be 1.013e5 Pa)

____m

This is my FOURTH time submitting this question. The answer IS NOT .018 or .019. Here is the hint they gave:

See if you can write an expression that shows how the pressure due to a column of two fluids depends on the weight of the fluids in the column and the cross-sectional area of the column. How is the pressure at the bottom of the container related to the pressure due to the weight of the fluids and atmospheric pressure?

Answer 1

Suppose the pressure at the bottom of the cylinder is given by:

P = rho_m*g*d + rho_w*g*d1 + Patm

where

d = depth of the mercury

d1 = height of water column above mercury = h - d

where, h = height of cylinder = 0.8 m

rho_m = density of mercury = 1.36*10^4 kg/m^3

rho_w = density of water = 1000 kg/m^3

Patm = atmospheric pressure = 1 atm = 1.01325*10^5 Pa

P = Pressure at bottom = 1.1 atm = 1.11457*10^5 Pa

So,

P = rho_m*g*d + rho_w*g*d1 + Patm

P = rho_m*g*d + rho_w*g*(h - d) + Patm

Using given values:

1.11457*10^5 = 1.36*10^4*9.81*d + 1000*9.81*(0.8 - d) + 1.01325*10^5

Solving above equation

d = 0.018 m

try the answer as d = 0.02 m (maybe you need answer in 1 significant digit)

Please check that answer should be 0.018 m, Let me know the correct answer whenever you get it. Please do not downvote before that.

Let me know if it works.