Question on bernoulli's equation

In summary, the conversation discusses a problem involving a mercury manometer measuring pressure difference in a water-filled pipe. The goal is to find the height h. There is a discrepancy in the professor's solution, as they assume pressure does not depend on height in water. However, the correct solution takes into account the distance from the center line where pressure changes. The revised solution gives a relationship between P1, P2, and h, resulting in a height of 56cm.
  • #1
theBEAST
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0

Homework Statement


This is from the notes given to my professor and I think that it may be incorrect:
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Essentially we have a mercury manometer that measures the pressure difference at points 1 and 2. The fluid flowing through the pipe is water. The goal is to find the height h. Now in these notes, my professor seems to be assuming that the pressure does not depend on the height in the water. This is because on the last line he wrote rho_Hg * g * h = P_1. However I think the distance used should be from the center line since the pressure changes?

Also the pressure he solved for, P_1 = 11.3kPa (which I think is wrong), is the pressure at the streamline? This is wrong because we want to use the pressure RIGHT above the mercury.EDIT: I redid the question and found P1 = 69420Pa. Then I found a relationship between P1, P2 and h:

P2 = P1 + rho_w * g * h - rho_Hg * g * h
0 = 69420 + 9.81 * h * (1000 - 13600)

Solving for h I get 56cm.
 
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  • #2
The 69420 Pa is for the pressure difference:

P1 - P2 = 69420 Pa

The pressure at 2 is not 0, the water is still in the pipe. It is only when it emerges that the pressure is 0. The height difference of columns of mercury in the manometer is due to this pressure difference. So one sets this pressure difference equal to

ρHggh = 69420

for which I get 52 cm?
 
  • #3
Basic_Physics said:
ρHggh = 69420

for which I get 52 cm?
You have not allowed for the fact that the portion of the manometer pipe that is not filled with mercury is filled with water. The density difference is 12600, giving the 53cm in the OP.
 

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid dynamics that relates the velocity, pressure, and potential energy of a fluid along a streamline. It states that the sum of the kinetic energy, potential energy, and pressure energy of a fluid remains constant at all points along a streamline.

2. What is the significance of Bernoulli's equation in fluid mechanics?

Bernoulli's equation is significant in fluid mechanics because it helps us understand and predict the behavior of fluids in motion. It is used in various applications such as designing aircraft wings, calculating water flow in pipes, and understanding weather patterns.

3. What are the assumptions made in Bernoulli's equation?

The assumptions made in Bernoulli's equation are that the fluid is incompressible, the flow is steady, the fluid is inviscid (no friction), and the energy losses due to heat and sound are negligible.

4. How is Bernoulli's equation derived?

Bernoulli's equation can be derived from the principles of conservation of mass and energy. By applying these principles to a small volume of fluid along a streamline, we can express the change in kinetic energy, potential energy, and pressure energy in terms of each other, resulting in the equation.

5. Can Bernoulli's equation be applied to all fluids?

No, Bernoulli's equation can only be applied to incompressible fluids. Incompressible fluids are those whose density does not change with changes in pressure, such as water and air at low speeds. For compressible fluids, such as gases, the equation must be modified to account for changes in density.

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