The gauge pressure at the bottom of a vertical tube (open to the atmosphere) filled with mecury is 100kPa. How high is the column of mecury in the tube?

I used the formula pressure=density * gravity * height which i reaaranged to find h= 100000Pa/(13570kg/m3*9.8)=0.75m but this is not the correct answer, can anyone help me out

100 kPa is 0.987 atm. If that is the gauge pressure there, the absolute pressure there is 1.987 atm.

I agree with your answer.

To solve this problem, you are on the right track with the formula pressure = density * gravity * height. However, your calculation seems to be incorrect.

Let's go through the steps again to calculate the correct answer:

1. Pressure: The gauge pressure at the bottom of the tube is given as 100 kPa. However, the pressure at the bottom of the tube is equal to the atmospheric pressure plus the gauge pressure, since the tube is open to the atmosphere. Atmospheric pressure is approximately 101.3 kPa. So, the absolute pressure at the bottom of the tube is (101.3 kPa + 100 kPa) = 201.3 kPa.

2. Density: The density of mercury is given as 13,570 kg/m^3.

3. Gravity: The acceleration due to gravity, denoted as "g," is approximately 9.8 m/s^2.

Now, let's rearrange the equation to solve for height:

height = pressure / (density * gravity)
= (201300 Pa) / (13570 kg/m^3 * 9.8 m/s^2)
≈ 1.46 meters

Therefore, the column of mercury in the tube is approximately 1.46 meters high.