Fluid Statics- u-tube displacement

[helppls]

Homework Statement

A uniform U-tube is partially filled with water (ρH20 = 1000 kg/m3). Oil, of density 750 kg/m3, is poured into the right arm until the water level in the left arm rises 30 mm. The length of the oil column is then: (Answer: 40mm)

Homework Equations

P = pgh
Pressure = density x gravity x height

The Attempt at a Solution

Hi, I originally calculated this with a displacement of 30mm and calculated the correct answer (40mm), but when I re-did my FBD I found that the displacement should be 60mm because the water goes up 30mm on the LHS and down 30mm on the RHS, so my answer of 80mm was incorrect. The teacher has said that the question is very clear about the displacement being 30mm. Can you please explain why?

H H20 = 30+30 = 60mm = h1
pH20 = 1000 kg/m^3
PH20 = pH20 * h1

H Oil = h2 = ?
pOil = 750 kh/m^3
POil = pOil * h2

Ph20 = POil
rearrange to get
h2 = (pH20 * h1 )/ pOil
= (1000 * 60)/750 = 80mm = height of oil

but the answer is 40mm because a displacement of 30mm should be used?

 

[TSny]

I think I follow your work. You are using lower case p for density and capital P for pressure. And you aren't bothering with including the acceleration of gravity g in the pressure as it will cancel out anyway?

I agree with your answer of 80 mm. As you say, if the top of the water goes up 30 mm on the left then the top of the water must go down 30 mm on the right. The difference in position of the top of the water on the two sides is 60 mm.

 

[helppls]

I think I follow your work. You are using lower case p for density and capital P for pressure. And you aren't bothering with including the acceleration of gravity g in the pressure as it will cancel out anyway?

I agree with your answer of 80 mm. As you say, if the top of the water goes up 30 mm on the left then the top of the water must go down 30 mm on the right. The difference in position of the top of the water on the two sides is 60 mm.

Thank you so much. Upon review my answer of 80mm was also accepted and marks corrected.