Fluid Mechanics: Weight vs Pressure

In summary, the conversation discusses the equilibrium of a thin uniform circular tube containing two non-miscible liquids with densities a and b, respectively. The ratio of densities a/b is equal to 3.732 and the concept of using weights to determine equilibrium is flawed. The correct approach is to use dp/dz=-ρg and equate the pressures at the interface. It is also mentioned that the bottom of the curved tube wall supports part of the weight of each fluid.
  • #1
Prannoy Mehta
94
2

Homework Statement



A thin uniform circular tube is kept in a vertical plane. Equal volumes of (The liquids subtend a right angle at the centre) two non miscible liquids whose densities are a and b respectively fill half of the tube as shown. (The diagram depicts a>b) In equilibrium the radius passing through the interface makes an angle of 30 degrees with the vertical. The ratio of densities a/b is equal to.

Homework Equations



The basic equations of fluid mechanics given in any introductory course.

The Attempt at a Solution



I tried equating the weights on both the side as it must be necessary condition for the equilibrium.
Doing so I have obtained the answer as 3. The answer given in the text is 3.732. Where is the flaw in my concept.

Thanks for all the help.
 
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  • #2
How can a tube be kept in a plane?
Is the tube lying on its side or standing on end?
I think we need to see the diagram.
 
  • #3
I thought it was not required, sorry for the trouble..

upload_2015-10-24_16-8-10.png
 

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  • #4
The flaw in your logic us using the weights. You ought to be using dp/dz=-ρg, and equating the pressures at the interface.

Chet
 
  • #5
I still did not understand why that concept of weight is wrong, for equilibrium the weight of the liquid with density a, subtending 60 degrees at the centre, should be equal to that, of the a subtending 30 degrees, and the liquid b which is subtending 90 degrees. I do realize there is a flaw in that concept, just wanted to know what is the flaw..

PS: I got the answer using that method. Thank you :)
 
  • #6
Prannoy Mehta said:
I still did not understand why that concept of weight is wrong, for equilibrium the weight of the liquid with density a, subtending 60 degrees at the centre, should be equal to that, of the a subtending 30 degrees, and the liquid b which is subtending 90 degrees. I do realize there is a flaw in that concept, just wanted to know what is the flaw..
You are aware that the bottom of the curved tube wall supports part of the weight of each fluid, correct?

Chet
 
  • #7
Yes, I got it now. I din't think of it that perspective.
 

Related to Fluid Mechanics: Weight vs Pressure

1. What is the difference between weight and pressure in fluid mechanics?

Weight in fluid mechanics refers to the gravitational force exerted on a fluid due to its mass. It is measured in units of force, such as Newtons or pounds. Pressure, on the other hand, is the force per unit area exerted by a fluid on its surroundings. It is measured in units of force per unit area, such as Pascals or pounds per square inch. In other words, weight is the force of gravity on a fluid, while pressure is the force that a fluid exerts on a surface.

2. How are weight and pressure related in fluid mechanics?

Weight and pressure are related in fluid mechanics through the concept of density. Density is defined as the mass per unit volume of a substance. In a fluid, weight is directly proportional to density, meaning that the more dense a fluid is, the more weight it will have. Pressure, on the other hand, is inversely proportional to density, meaning that as density increases, pressure decreases. This is why fluids with a higher density, such as water, exert more pressure on their surroundings than less dense fluids, such as air.

3. How does depth affect weight and pressure in fluid mechanics?

In fluid mechanics, depth plays a crucial role in determining weight and pressure. As a fluid gets deeper, its weight increases due to the increased amount of fluid above it. However, the pressure at a particular depth does not depend on the weight of the fluid above it, but rather on the depth itself. This is because the weight of the fluid above a certain depth is balanced by the weight of the fluid below, resulting in a constant pressure at that depth.

4. What is the difference between static and dynamic pressure in fluid mechanics?

Static pressure in fluid mechanics refers to the pressure exerted by a fluid when it is at rest. This is the pressure that a fluid exerts on its surroundings, such as the walls of a container. Dynamic pressure, on the other hand, is the pressure exerted by a fluid in motion. This is the pressure that a fluid exerts on an object moving through it, such as an airplane wing or a boat hull. In both cases, the pressure is caused by the fluid's weight and its velocity.

5. How does fluid viscosity affect weight and pressure in fluid mechanics?

Fluid viscosity, or its resistance to flow, has a significant impact on weight and pressure in fluid mechanics. In a fluid with high viscosity, such as honey, the fluid molecules are tightly packed and move slowly, resulting in a higher weight and pressure. In contrast, in a fluid with low viscosity, such as water, the molecules are more spread out and move more freely, resulting in a lower weight and pressure. This is why more viscous fluids exert more pressure on their surroundings than less viscous fluids at the same depth and velocity.

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