Calculating Liquid Height Difference in U-Tube | Fluid Mechanics Homework

AI Thread Summary
To find the height difference in a U-tube containing water and oil, the pressures at the liquid interface must be equal. The equation P = gph is used, where P represents pressure, g is the acceleration due to gravity, p is the density of the liquid, and h is the height. The oil has a density 80% that of water, leading to two unknown heights to solve for. By establishing the relationship between the heights of the oil and water columns, the difference in height can be calculated. The discussion emphasizes understanding pressure equilibrium in fluid mechanics to solve the problem effectively.
bennyq
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Homework Statement



One hundred millilitres of water is poured into a U-tube that has a cross-sectional area of 1 cm2. Then 100 millilitres of oil, with a density 80% that of water, is poured down one side of the U-tube so that the oil floats on the water. Find the difference in height of the liquid surfaces on the two sides of the U-tube.

Homework Equations


P=gph


The Attempt at a Solution


Just struggling to get started, i know that on either side that at a certain point the pressures are equal.
Just a pointer to get going would be great..
 
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bennyq said:

Homework Statement



One hundred millilitres of water is poured into a U-tube that has a cross-sectional area of 1 cm2. Then 100 millilitres of oil, with a density 80% that of water, is poured down one side of the U-tube so that the oil floats on the water. Find the difference in height of the liquid surfaces on the two sides of the U-tube.

Homework Equations


P=gph


The Attempt at a Solution


Just struggling to get started, i know that on either side that at a certain point the pressures are equal.
Just a pointer to get going would be great..

Match them up at the bottom of the U.

Chet
 
in my sketch, i have Pa = LHS p(oil)gh = RHS p(water)gL .. g cancels our but i have two unknowns..which is the different heights of each column?
 
bennyq said:
in my sketch, i have Pa = LHS p(oil)gh = RHS p(water)gL .. g cancels our but i have two unknowns..which is the different heights of each column?

If h is the height of the oil above the oil-water interface, and L is the height of the water above the oil-water interface, the h = 100 cm.

Chet
 
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ah okay, thank you chet
 
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