Solving Pressure Equilibrium Problem Involving Oil & Mercury

[PirateFan308]

Homework Statement

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 initially closed. Both containers are filled initially to the same height of h = 1.00m, the left with oil, and the right with mercury. The valve is then opened. Oil and mercury have densities of 6,000 kg/m3 and 13,600 kg/m3 , respectively. The oil and mercury do not mix.

Determine the fluid level in the left container when equilibrium is established again.

The Attempt at a Solution

Because mercury is more dense 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$= (101325) + (6000)(9.81)(1) = 160185 Pa$

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

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

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

$234741 - 133416h = 160185 + 133416h$

$74556 = 266832h$

$h=0.2794m$

So the fluid level of the left container equals 1.00+0.2794 = 1.2794. The site says that this is wrong but I can't find my mistake. I've checked the answer and the pressures on the bottom of both containers don't equal. I've tried to find the mistake but I really can't find it.

 

[Curious3141]

Homework Statement

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 initially closed. Both containers are filled initially to the same height of h = 1.00m, the left with oil, and the right with mercury. The valve is then opened. Oil and mercury have densities of 6,000 kg/m3 and 13,600 kg/m3 , respectively. The oil and mercury do not mix.

Determine the fluid level in the left container when equilibrium is established again.

The Attempt at a Solution

Because mercury is more dense 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$= (101325) + (6000)(9.81)(1) = 160185 Pa$

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

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

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

$234741 - 133416h = 160185 + 133416h$

$74556 = 266832h$

$h=0.2794m$

So the fluid level of the left container equals 1.00+0.2794 = 1.2794. The site says that this is wrong but I can't find my mistake. I've checked the answer and the pressures on the bottom of both containers don't equal. I've tried to find the mistake but I really can't find it.

I get the same answer you do. Your answer is right. Maybe try using less significant figures since this is a computer doing the checking.