Fluid Mechanics: Fluid in a Tube

In summary, the problem involves a U-shaped tube with one open and one closed arm, filled with a liquid of density 2.40 g/cm^3. The entire system is accelerated to the left at 2.5m/s^2. The pressure at point A, in the bottom right-hand corner of the tube, is calculated using the equation p=ρgh, where ρ is the density of the liquid, g is the pseudo-gravity acceleration, and h is the height of the liquid column. After calculating the pressures due to the vertical and horizontal columns, the total pressure at point A is found to be 5.4 kPa.
  • #1
rdelane1
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Homework Statement



The problem depicts a tube shaped like a "U". The arms of the tube are 0.3m in height and the horizontal part of the tube is 0.6m long. The left arm of the tube is open while the right arm of the tube is closed. The problem states that the liquid in the tube is of density 2.40 g/cm^3. The problem then states that the whole system is accelerated to the left at 2.5m/s^2. The problem asks for the pressure at point A, in the bottom right-hand corner of the tube.

Homework Equations



I am assuming that one component of the pressure at point A is due to hydrostatic pressure, so p=ρgh. The problem doesn't mention atmospheric pressure so I am assuming the problem is in terms of gage pressure.

The Attempt at a Solution



So far the only thing I can come up with is to calculate the hydrostatic pressure in the vertical and horizontal direction, since acceleration is like acceleration due to gravity in the vertical direction. Adding the two together I got approx. 10.7kpa which seems reasonable.
 
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  • #2


Hello,

Your approach to the problem is correct. Since the tube is being accelerated to the left, the liquid in the tube will experience a pseudo-gravity force in the same direction. This will result in a hydrostatic pressure gradient along the vertical and horizontal arms of the tube.

To calculate the pressure at point A, you can use the equation p=ρgh, where ρ is the density of the liquid, g is the pseudo-gravity acceleration (in this case, 2.5m/s^2), and h is the height of the liquid column.

First, calculate the pressure due to the liquid column in the vertical arm of the tube. Since the height of the liquid column is 0.3m, the pressure at point A due to the vertical column will be p=2.40g/cm^3 * 0.3m * 2.5m/s^2 = 1.8 kPa.

Next, calculate the pressure due to the liquid column in the horizontal arm of the tube. Since the length of the horizontal arm is 0.6m, the pressure at point A due to the horizontal column will be p=2.40g/cm^3 * 0.6m * 2.5m/s^2 = 3.6 kPa.

Finally, add these two pressures together to get the total pressure at point A: 1.8 kPa + 3.6 kPa = 5.4 kPa.

Therefore, the pressure at point A is 5.4 kPa. This includes both the hydrostatic pressure and the additional pressure due to the acceleration of the tube.

Hope this helps!
 

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids (liquids and gases) and their properties, such as how they flow and behave under different conditions.

2. What is meant by a fluid in a tube?

A fluid in a tube refers to a fluid that is confined to flow within a tube or pipe under the influence of some external force, such as pressure or gravity.

3. What is the significance of studying fluid in a tube?

Studying fluid in a tube is important because it helps us understand the behavior of fluids in closed systems, which is crucial for many practical applications such as designing pipelines, pumps, and hydraulic systems.

4. How is fluid mechanics used in engineering?

Fluid mechanics is used in engineering to analyze and predict the behavior of fluids in various systems, such as turbines, heat exchangers, and aircraft wings. It helps engineers design efficient and safe systems that involve the use of fluids.

5. What are some real-world examples of fluid in a tube?

Examples of fluid in a tube include water flowing through pipes in a plumbing system, oil being transported through a pipeline, and blood flowing through blood vessels in the human body.

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