How High Does Mercury Rise in a U-Tube When Water is Added?

  • Thread starter Thread starter Phyeng
  • Start date Start date
  • Tags Tags
    Pressure Tube
Click For Summary
SUMMARY

The discussion centers on the calculation of how high mercury rises in a U-tube when 2.0 cm of water is added to one arm. The correct answer is determined to be 0.0714 cm, which represents the height the mercury rises in the right arm after achieving equilibrium. The calculation involves applying the principle of hydrostatic equilibrium, where the density of mercury (14 × 103 kg/m3) and water (1.0 × 103 kg/m3) are used to derive the height difference. The initial miscalculation of 0.143 cm is clarified as the total height difference, not the rise in the right arm.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Knowledge of fluid density and its impact on equilibrium
  • Familiarity with basic algebra for solving equations
  • Concept of U-tube manometers in fluid mechanics
NEXT STEPS
  • Study hydrostatic pressure calculations in U-tube systems
  • Learn about the principles of fluid equilibrium in physics
  • Explore the applications of manometers in measuring pressure differences
  • Review density and buoyancy concepts in fluid mechanics
USEFUL FOR

Students studying physics, particularly those focusing on fluid mechanics, as well as educators teaching hydrostatics and related concepts.

Phyeng
Messages
1
Reaction score
0

Homework Statement


A long U-tube contains mercury (density = 14 × 103 kg/m3). When 2.0 cm of water (density = 1.0 × 103 kg/m 3) is poured into the left arm, the mercury in the right arm rises above its original level by


Homework Equations


Density*gravity*height(on the left arm)=density*gravity*height(on the right arm)


The Attempt at a Solution


Using the above equation I got the answer 0.143cm(rounded) but that isn't the final answer.because 0.143 cm is the height difference between two sides of the mercury.
I think the answer is 0.071cm because if 0.14cm of fluid moved to the right arm and to put this tube back into equilibrium, half of that fluid that has to move from right side to the other side? therefore if half of 0.143 moved to the other side, then the distance moved from original poistion would be 0.143-(0.143/2)=0.071.
I am not sure if this is right, But if it sounds right to anyone, please say so, so i can be sure that I'm right. Thanks you very much for spending time to read, Very much appreciated.
 
Physics news on Phys.org
NO YOU ARE WRONG.THE EQUATIONS APPLIED BY YOU GIVE DIRECTLY THE FINAL STATE IN EQUILIBRIUM.THE FINAL ANSWER 0.143=DISTANCE TRAVELED BY MERCURY IN LEFT ARM (DOWNWARDS)+DISTANCE TRAVELED BY MERCURY IN RIGHT ARM(UPWARDS).
AS THE QUESTION IS "mercury in the right arm rises above its original level by" THUS ANSWER IS 0.0714
 

Similar threads

Pressure-related problem with Mercury and Water in a U-tube
  • · Replies 18 ·
Replies
18
Views
7K
How Do Viscous Interactions Differ in Vertical and Horizontal Geometries?
  • · Replies 31 ·
2
Replies
31
Views
4K
How Does a Fluid Oscillate in a U-Tube with Mercury?
  • · Replies 2 ·
Replies
2
Views
3K
Calculating Mercury Column Height in J-Shaped Tube: Manometry Homework Solution
  • · Replies 7 ·
Replies
7
Views
2K
Pressure measurement in U tube with mercury and water
  • · Replies 3 ·
Replies
3
Views
4K
High School Why does mercury rise in a glass capillary tube despite its strong cohesion?
  • · Replies 3 ·
Replies
3
Views
3K
Calculating Rise of Mercury in U-tube with Water
  • · Replies 1 ·
Replies
1
Views
4K
Fluid Statics- u-tube displacement
  • · Replies 2 ·
Replies
2
Views
7K
U-Tube Fluid Statics: Solving for Water Column Length and Mercury Rise
  • · Replies 4 ·
Replies
4
Views
4K
Calculating Work Done by Gas in a Mercury-Filled U-Tube with Right Angle Bends"
  • · Replies 10 ·
Replies
10
Views
3K