Density of a liquid above a column of water

Click For Summary
SUMMARY

The discussion centers on calculating the density of an unknown liquid supported by a column of water. The pressure equilibrium condition is established using the equation h1ρ1g = h2ρ2g, where h1 and h2 are the heights of the water and the unknown liquid, respectively, and ρ1 and ρ2 are their densities. Participants emphasize that for the columns to remain in equilibrium, the pressures exerted by both liquids at their interface must be equal, adhering to the principles of fluid mechanics and Bernoulli's equation. The conversation clarifies the interaction of forces at the interface, reinforcing the concept of action and reaction in fluid dynamics.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly pressure equilibrium.
  • Familiarity with Bernoulli's equation and its applications.
  • Basic knowledge of density and its calculation in fluid systems.
  • Ability to manipulate and solve algebraic equations involving physical quantities.
NEXT STEPS
  • Study the derivation and applications of Bernoulli's equation in fluid dynamics.
  • Learn about hydrostatic pressure and its implications in fluid columns.
  • Explore the concept of pressure transmission in fluids and its relevance to equilibrium.
  • Investigate the principles of action and reaction forces in fluid systems.
USEFUL FOR

Students studying fluid mechanics, physics enthusiasts, and anyone involved in engineering or scientific fields that require an understanding of fluid behavior and pressure dynamics.

takando12
Messages
122
Reaction score
5

Homework Statement


A column of water 40 cm high supports a 30 cm column of an unknown liquid.What is the density of the liquid?

Homework Equations

The Attempt at a Solution


As per the instruction of the teacher I equated their pressures.
h1ρ1g=h2ρ2g. And hence arrived at the answer. But I don't understand why we are doing this.Why should the pressures of both the columns be equal? I am trying to think of what would happen if they weren't equal but I can't get it. The unknown liquid column will be acted on by atmospheric pressure at the top. What will the pressure at the interface of the 2 liquids be?
 
Physics news on Phys.org
takando12 said:
Why should the pressures of both the columns be equal?
Where the two meet, right?
If the pressure in one is P and the cross sectional area where they meet is A then what force does it exert on the other fluid? What will happen if they push on the interface area with unequal forces?
 
Any total pressure difference that not satisfy Bernoulli's equation make fluid acceleration. For unmoved liquid, pressure on the same label must be the same.
 
ok. So for the columns to remain in equilibrium, the pressures(or forces) they exert on each other should be equal.
the first column exerts pressure on the second at the interface, but i thought the second only exerts pressure on the bottom of the container? but it actually does on the first.
 
takando12 said:
ok. So for the columns to remain in equilibrium, the pressures(or forces) they exert on each other should be equal.
the first column exerts pressure on the second at the interface, but i thought the second only exerts pressure on the bottom of the container? but it actually does on the first.
They must exert pressure on each other at the interface. Action and reaction.
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
Replies
16
Views
6K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K