Question

Two identical containers are open at the top and are connected at the bottom via a tube of negligible volume and a valve that is closed. Both containers are filled initially to the same height of 1.00 m, one with water, the other with mercury, as the drawing indicates. The valve is then opened. Water and mercury are immiscible. Determine the fluid level in the left container when equilibrium is reestablished.

Answer 1

Because mercury is denser than oil, some of the mercury will transfer to the left container and the pressure at the bottom of the left container must equal the pressure at the bottom of the right container.

Pressure between oil and mercury on left container =(101325)+(6000)(9.81)(1)=160185Pa

Pressure on the bottom of the left container = 160185 + ( 13600 ) ( 9.81 ) ( h ) = 160185 + 133416 h

Pressure on the bottom of the right container = 101325 + ( 13600 ) ( 9.81 ) ( 1 ? h ) = 101325 + 133416 ? 133416 h = 234741 ? 133416 h

Pressure on the bottom of the right container must equal the pressure on the bottom of the left container :

234741 ? 133416 h = 160185 + 133416 h

74556 = 266832 h

h = 0.2794 m