# Fluid Statics- u-tube displacement

• helppls
In summary, the conversation discusses a problem involving a uniform U-tube partially filled with water and oil. After pouring oil into the right arm, the water level in the left arm rises 30 mm. The length of the oil column is then determined to be 40mm. After some calculations, the answer is found to be 80mm, but it is clarified that a displacement of 30mm should be used instead, resulting in the correct answer of 40mm. The conversation also includes a discussion about the use of capital and lowercase letters for density and pressure, as well as the inclusion of acceleration of gravity in the pressure calculation.
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?

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.

TSny said:
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.

## 1. What is fluid statics?

Fluid statics is the branch of fluid mechanics that deals with fluids at rest and the forces acting on them.

## 2. What is a u-tube displacement?

A u-tube displacement is a type of fluid displacement experiment in which a u-shaped tube is filled with a fluid and then a second fluid is added to one side, causing the first fluid to move and create a measurable height difference between the two sides of the tube.

## 3. How does a u-tube displacement work?

A u-tube displacement works by utilizing the principle of fluid pressure. When a second fluid is added to one side of the u-tube, the pressure of the first fluid decreases, causing it to rise on the other side of the tube. The difference in height between the two sides is directly proportional to the difference in pressure between the two fluids.

## 4. What is the purpose of a u-tube displacement experiment?

The purpose of a u-tube displacement experiment is to demonstrate the effects of fluid pressure and to measure the density of a fluid. By measuring the height difference of the two fluids in the u-tube, the density of the first fluid can be calculated using the equation P = ρgh, where P is pressure, ρ is density, g is the acceleration due to gravity, and h is the height difference.

## 5. What are some real-world applications of u-tube displacement?

U-tube displacement experiments are commonly used in the fields of hydraulics and fluid mechanics, as well as in industries such as oil and gas, chemical engineering, and environmental science. They are also used in medical settings, such as for measuring blood pressure and determining the density of bodily fluids.

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