Fluid mechanics question

In summary, the left arm of a tube has a corss sectional area A1 of 10.0cm^2 and the right arm has a cross sectional area of A2 = 5.00cm^2. 100g water are poured into the right arm. b) givent he density of mercury is 13.6g/cm^3, what distance 'h' does the mercury rise in the left arm? I worked out in question 'a' that the length of the column of water is 20cm. With this, I used Pnot + densityofmercury*g*Hmercury = Pnot + densityofwater*g*Hwater. This gives me the Hmer
  • #1
vcc
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There is a question that I have been stumped on for a while now.

it is as follows:

"The left arm of a tube has a corss sectional area A1 of 10.0cm^2 and the right arm has a cross sectional area of A2 = 5.00cm^2.

100g water are poured into the right arm.

b) givent he density of mercury is 13.6g/cm^3, what distance 'h' does the mercury rise in the left arm?

I worked out in question 'a' that the length of the column of water is 20cm.

With this, I used Pnot + densityofmercury*g*Hmercury = Pnot + densityofwater*g*Hwater

This gives me the Hmercury displaced on the right arm.

With that displacement, which I calculated to be Hmercury = 1.47cm, I can calculate the displacement on the left side.

V1=A1H1 <volume of displacement1\____should be equal
V2=A2Hmercury <volume of displacement2/

V1 = V2

therefore A2(1.47cm)/A1 = H1

I calculated H1 to be 0.735cm or 7.3mm

However, this answer is wrong. THe correct answer is 4.9mm

Why is this?? I am truly frustrated and stumped:grumpy:
 
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  • #2
I'd appreciate some form of a reply. That way I know what to change in the phrasing of the above post.
 
  • #3
I have tried my hand at it for more than an hour - no luck yet - got it ! It needs a detailed drawing which takes some time to approve so here goes...
The general idea is still to compare the pressures in the two arms at the height of the bottom of the water column. The height of the displaced mercury volume [itex]\Delta V[/itex] in the right arm comes to
[tex]h'=h\frac{A_1}{A_2}[/tex]
the height of the column in the left arm that we want to compare with the water column is then given by
[tex]h+h'[/tex]
comparing the pressures then gives [itex]h[/itex].
 

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  • #4
andrevdh said:
I have tried my hand at it for more than an hour - no luck yet - got it watch this space - it needs a detailed drawing which takes some time to aprove so here goes...
The general idea is still to compare the presure in the two arms at the height of the bottom of the water column. The height of the displaced mercury volume [itex]\DeltaV[/itex] in the right arm comes to
[tex]h'=h\frac{A_1}{A_2}[/tex]
the height of the column in the left arm that we want to compare with the water column is then given by
[tex]h+h'[/tex]
comparing the pressures then gives [itex]h[/itex].
Thanks for the help and effort btw. I appreciate it
 

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids and their properties, such as their motion, behavior, and interactions with other substances.

2. What are the different types of fluids?

The two main types of fluids are liquids and gases. Liquids have a definite volume but can change shape, while gases have neither a definite volume nor shape.

3. What is the difference between laminar and turbulent flow?

Laminar flow is a smooth, orderly flow of fluid, while turbulent flow is chaotic and unpredictable. Laminar flow occurs at low velocities and is characterized by layers of fluid moving parallel to each other, while turbulent flow occurs at high velocities and is characterized by mixing and eddies.

4. How is Bernoulli's principle related to fluid mechanics?

Bernoulli's principle states that as the velocity of a fluid increases, its pressure decreases. This principle is important in understanding the lift force of airplane wings and the flow of fluids through pipes and nozzles.

5. What are some real-world applications of fluid mechanics?

Fluid mechanics has many practical applications in everyday life, such as in the design of airplanes, cars, and ships. It is also important in the study of weather patterns, ocean currents, and the movement of blood through the human body.

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