Multi Tube and fluid pressure

In summary, we have two fluids (water and oil) in a tube with one side open to the atmosphere. By using the principle of equal pressure at the same depth, we can set up equations to solve for the density of the oil, which is found to be smaller than the density of water.
  • #1
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Homework Statement


Now two fluids are placed in the same tube (d). Both sides are open to the atmosphere without pistons. One fluid is water and the other (on top of the water in the left branch of the tube) is an oil of unknown density. l = 135mm and d = 12.3mm. What is the density of the oil?
Image here:
http://screencast.com/t/ZGEwODAy

Homework Equations



change in pressure=density*g*h

The Attempt at a Solution



I'm not sure how to start. I feel this is going to be the hardest topic for me to grasp
 
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  • #2
Ok so start by looking at the picture. Look at the depth d + l. On the right side you have the atmosphere and some water pressing down at that point. On the left side you have the atmosphere and oil (more than the amount of water pressing down on the right). Therefore we expect the density of the oil to be smaller than water.

One of the principles of fluid mechanics is that the same liquid will have the same pressure at the same depth. For example, let's look at the water at depth d + l.

On the right side the pressure is this:

[tex] P = P_{atm} + \rho_{water}g(0.135 m) [/tex]

On the left side the pressure is this:

[tex] P = P_{atm} + \rho_{oil}g(0.135 m + 0.0123 m) [/tex]

Set the two equations equal to each other and solve for [tex] \rho_{oil} [/tex]
 

1. What is multi tube and fluid pressure?

Multi tube and fluid pressure is a scientific concept that describes the behavior of fluids, such as liquids and gases, when they are confined in multiple tubes or channels. It refers to the force exerted by a fluid on the walls of its container, which is caused by the random motion of its molecules.

2. How is fluid pressure affected by the number of tubes?

The number of tubes has a direct impact on fluid pressure. As the number of tubes increases, the pressure exerted by the fluid also increases. This is because the force exerted by the fluid is distributed over a larger surface area, resulting in a higher overall pressure.

3. What factors influence multi tube and fluid pressure?

Several factors can influence multi tube and fluid pressure, including the type of fluid, the temperature, the volume of the fluid, and the shape and size of the tubes. Additionally, external factors such as gravity and atmospheric pressure can also affect fluid pressure.

4. How is multi tube and fluid pressure measured?

Multi tube and fluid pressure can be measured using instruments such as manometers, barometers, and pressure gauges. These instruments use different techniques to measure the pressure exerted by a fluid, such as the height of a column of liquid, the deflection of a spring, or the force required to compress a gas.

5. What are the practical applications of understanding multi tube and fluid pressure?

Understanding multi tube and fluid pressure is crucial in various fields, including engineering, medicine, and environmental science. It helps in the design and operation of hydraulic systems, the diagnosis of medical conditions, and the study of weather patterns and ocean currents, among others.

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