Find out the correct pressure difference if the level of the liquid

[zorro]

Homework Statement

The limbs of a manometer consist of uniform capillary tubes of radii 1.4 x 10^-3 m and 7.2 x 10^-4 m. Find out the correct pressure difference if the level of the liquid (density 10^3 kg/m^3 and surface tension 72 x 10^-3 N/m) in narrower tube stands 0.2 m above that in the broader tube.

Homework Equations

The Attempt at a Solution

Please explain me the meaning of this question. Why is there a false pressure difference?
The manometer measures the pressure of a gas. So it ought to show the correct pressure.

 

[rl.bhat]

The difference between the liquid levels is due to pressure difference due to the liquid and surface tension.
So 0.2 m = ρ*g*h + 2*T/ρ*g*r.

Hence correct pressure difference = ρ*g*h = 0.2 - 2*T/ρ*g*r.

 

[zorro]

so the only error is due to surface tension?

 

[rl.bhat]

so the only error is due to surface tension?

Yes.

 

[rwisz]

What is the significance of the liquid level in this scenario?The question is asking for the correct pressure difference between the two tubes of the manometer, given the specific dimensions and properties of the tubes and the liquid being used. The significance of the liquid level is that it is used to measure the pressure difference between the two tubes. The manometer works by balancing the pressure of the gas being measured with the pressure of the liquid in the tubes. The difference in the level of the liquid in the two tubes indicates the pressure difference between them.

As for the false pressure difference, it is possible that the measurements or calculations used to determine the pressure difference may not be accurate, leading to an incorrect value. This could be due to errors in measurement, assumptions made in the equations used, or other factors. It is important for scientists to carefully consider and verify their results to ensure accuracy and avoid false conclusions.