Question

Two identical containers are open at the top and are connected at the bottom via a...

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.

for simplicity, assume the tanks have a cross section of 1 square meter.

mass of 1 cubic meter of water is about 998 kg, or 998*9.8 = 9780 Newtons so the pressure in the bottom of the tank is 9.78k pa

mass of 1 cubic meter of Hg is 13570 kg, weight is that * 9.8 or 133 kN
for a pressue of 133 Pa

This pressure difference causes mercury to flow into the water tank until pressures are equalized, with a height in the water tank h

Total mass = 13570 + 998 = 14570 kg, or weight of 142800 Newtons
this will equalize between the two containers at 71400 N or 7280 kg in each side.

the 7280 kg will consist of 998 kg of water with a height of 1 meter, and 6280 kg of mercury. 6280 kg / 13570 kg/m³ = 0.462 m³ of Hg.

So, the water tank will have 1 meter of water and 0.462 meter of Hg, total 1.462 meter. The Hg tank will have the rest of the mercury, or 0.537 meter

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