Fluid mechanics - Pascal's principle

In summary, in this conversation, the question asks for the distance the mercury rises in the left arm of a U-tube when 100 grams of water is poured into the right arm. The equation used to solve this problem is P=P(o)+ρgh, where ρ is the density of the subject in question. Using this equation and taking into account Pascal's law, the solution is found by equating the head pressure of the mercury and water at the original height of the mercury.
  • #1
muhammed_oli
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Homework Statement


Mercury is poured into a U-tube as shown in Figure a. The left arm of the tube has cross-sectional area A1 of 9.4 cm2, and the right arm has a cross-sectional area A2 of 4.50 cm2. One hundred grams of water are then poured into the right arm as shown in Figure b.
(b) Given that the density of mercury is 13.6 g/cm3, what distance h does the mercury rise in the left arm?

Homework Equations


P=P(o)+ρgh where ρ is density of subject in question

The Attempt at a Solution


Hey everyone, just need a little conceptual help here. I'm unsure how to find the height of the water and the reasoning behind it.
My equation is ρhggh = ρwghw
where hw is the height of water in the tube above the line. The volume displaced is equal, I'm that far but how does the water above the line factor into the calc? Or just set me straight for this, it seems the more I think about it the further I get from an answer, there's something I need to equate conceptually which I am not getting.
 

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  • #2
Your equation is correct. Think about it this way: Using the original height of the mercury as the base line, the head pressure at that base line on the mercury side and the water side will be equal (a portion of Pascal's law).
 
  • #3
thanks, worked through and got it
 

1. What is Pascal's principle in fluid mechanics?

Pascal's principle states that when a fluid is confined within a closed container, any change in pressure applied to the fluid will be transmitted equally in all directions throughout the fluid.

2. How does Pascal's principle apply to hydraulic systems?

In hydraulic systems, Pascal's principle is utilized to generate force by applying pressure to a small surface area, which is then transmitted to a larger surface area, resulting in a larger force.

3. What is the equation for calculating pressure in a fluid using Pascal's principle?

The equation is P = F/A, where P is pressure, F is force, and A is the surface area on which the force is applied.

4. Can Pascal's principle be applied to gases as well as liquids?

Yes, Pascal's principle can be applied to both gases and liquids. It is a fundamental principle of fluid mechanics that applies to any substance that can flow.

5. What are some real-life examples of Pascal's principle in action?

Pascal's principle can be observed in everyday life, such as in hydraulic car brakes, hydraulic jacks, and hydraulic lifts. It is also used in industrial processes, such as in hydraulic presses for shaping metals.

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