Mercury is added to a cylindrical container to a depth d and then the rest of th

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 0.4 m tall and the pressure at the bottom is 1.2 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36 x 104 kg/m3.) 94 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? m

Explanation / Answer

Let density of mercury be m = 1.36X104kg/m3

Let density of mercury be w = 1000kg/m3

Atmospheric pressure is 1 atmospheres = 101000N/m2

Pressure at the bottom of the container = atmospheric pressure + pressure due to mercury column + pressure due to water column

So, 1.2atmospheres = 1 atmosphere + mgd + wg(0.4-d)

or 0.2atmospheres = g[md + w(0.4-d)] =

or 0.2X101000N/m2 = 9.8m/s2[(13600kg/m3)d + (1000kg/m3)(0.4-d)]

2061.22 = 12600d + 400

or d = 0.1318m

So, depth of the mercury is  d = 0.1318m.

The pressure P due to the column of two fluids is:

P = mgd + wg(0.4-d)

Multiplying both sides by the cross sectional area A of the column we get:

PA = Admg + A(0.4-d)wg = Vmmg + Vwwg =Mmg + Mwg = Wm + Ww

or P = (Wm + Ww)/A

Where V, M and W denote the volume, mass and weight of the two columns.

Pressure at the bottom of the container = atmospheric pressure + pressure due to mercury column + pressure due to water column

So Pressure at the bottom of the container = atmospheric pressure + P

or Pressure at the bottom of the container = atmospheric pressure + (Wm + Ww)/A

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---