Question

1.Manometer fluid = Tungsten Hexafluoride WF6; Density = 13,000 g/m3; MW = 297.83 g/mol You have sent a probe to an unexplored planet and need to figure out what the gravity is on the planet before you can go there. The probe is equipped with a manometer that was calibrated on earth. Pressurized tanks are attached to each side with Tank A being a constant pressure. On earth, the Tank B was set to a pressure of 40 Pa which gave a height difference of 21 cm in the monometer fluid with the tank B side fluid being lower. The manometer was sent to the planet and where tank B pressure was set to 3.7 Pa. This gave a height difference of 6.1 cm with the fluid being higher on the tank B side. What is the gravity constant of the new planet? (Note: density of fluid will not change, and the fluid is immiscible with the other gases)

Answer 1

This problem can be solved by comparing the manometer equations in two different situations i.e at the earth and at an unexplored planet.

Manometer fluid density = 13000 g/m³ = 13000*10^-3 kg/m³

Considering the case in earth we develop an equation as follows:

Pa = a constant., Pb1= 40 Pa , h1= 21cm = 21*10^-2 m , g = 9.8 m/s² , rho = density of manometer fluid = 13000 *10^-3 kg/m³

Since level of fluid in tank B is lower it means that Pb1> Pa.

Therefore Pb1 - Pa = h1* (rho) * g

40- Pa = 21*10^-2 * 9.8 * 13000*10^-3 let it be equation 1

Next on on considering the case of unexplored planet the equation is as follows:

Pa = a constant., Pb2 = 3.7 Pa, h2 = 6.1cm = 6.1* 10^-2 m , let gravity constant in this planet be g _p which is to be found out.

rho remains the same for both planet.

Pa - Pb2 = h2* (rho)* g _p

Pa - 3.7= 6.1*10^-2 * g _p * 13000*10^-3 let it be equation 2

On addition of both equation 1&2 Pa get cancelled

We obtain 40 -3.7 = ( 13000*10^-3 *9.8* 21*10^-2) +

( 13000*10^-3 * g _p * 6.1* 10^-2)

Hence g _p can be found out by rearranging the above equation

And g _p is found to be 12.037 m/s²

Therefore gravity constant of new planet is found to be 12.037 m/s².