# Fluid Dynamics Question: A glass tube areas, pressure, determine height.

• ReMa
In summary: Then use the continuity equation to relate the velocities at those points. Finally, use the pressure equation to solve for the height h. In summary, the problem involves using the Bernoulli equation, continuity equation, and pressure equation to determine the height of mercury in a manometer with the given cross-sectional areas and flow velocity.
ReMa
http://home.cc.umanitoba.ca/~loly/102-dec_word.pdf
The above is a link to the problem - Question #3.

## Homework Statement

A glass tube has several different cross-sectional areas with the values indicated in the figure. A piston at the left end of the tube exerts pressure so that the mercury within the tube flows from the right end with a speed of 8.0 m/s. Three points within the tube are labeled A, B, and C.
Point A 12cm^2
Point B 5.6cm^2
Point C 6.0cm^2
NB: The drawing is not to scale.
Atmospheric pressure is 1.01×105 m/s2; and the density of mercury is 13 600 kg/m3.
Determine the height h of mercury in the manometer with the evacuated upper end.
(a) 136 mm (b) 269 mm (c) 276 mm (d) 366 mm (e) 371 mm

## Homework Equations

I really don't know where to start with this question, so any help would be appreciated here.

Atmospheric pressure is 1.01×105 m/s2
density of mercury is 13 600 kg/m3

Pressure = force / area, p = F/A

## The Attempt at a Solution

As above, not really sure where to start with this as I missed our week of learning about fluid dynamics and am now playing greaaat catch up. Would greatly appreciate the help!
--

Last edited:
ReMa said:
http://home.cc.umanitoba.ca/~loly/102-dec_word.pdf
The above is a link to the problem - Question #3.

## Homework Statement

A glass tube has several different cross-sectional areas with the values indicated in the figure. A piston at the left end of the tube exerts pressure so that the mercury within the tube flows from the right end with a speed of 8.0 m/s. Three points within the tube are labeled A, B, and C.
Point A 12cm^2
Point B 5.6cm^2
Point C 6.0cm^2
NB: The drawing is not to scale.
Atmospheric pressure is 1.01×105 m/s2; and the density of mercury is 13 600 kg/m3.
Determine the height h of mercury in the manometer with the evacuated upper end.
(a) 136 mm (b) 269 mm (c) 276 mm (d) 366 mm (e) 371 mm

## Homework Equations

I really don't know where to start with this question, so any help would be appreciated here.

Atmospheric pressure is 1.01×105 m/s2
density of mercury is 13 600 kg/m3

Pressure = force / area, p = F/A

## The Attempt at a Solution

As above, not really sure where to start with this as I missed our week of learning about fluid dynamics and am now playing greaaat catch up. Would greatly appreciate the help!
--
Start by applying the Bernoulli equation to the right end and the contracted center section.

## 1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (such as liquids and gases) behave when they are in motion. It involves understanding how fluids move, how they exert pressure, and how they interact with their surroundings.

## 2. How is the area of a glass tube related to fluid dynamics?

The area of a glass tube can affect the behavior of fluids inside it. A wider area allows for more fluid to flow through, while a narrower area can create more resistance and cause the fluid to move slower. This is known as the relationship between velocity and cross-sectional area.

## 3. How does pressure play a role in fluid dynamics?

Pressure is a key factor in fluid dynamics, as it is the force that drives the movement of fluids. Pressure is determined by the amount of force applied to a given area, and it can cause fluids to flow from areas of high pressure to areas of low pressure.

## 4. How is the height of a fluid determined in a glass tube?

The height of a fluid in a glass tube can be determined by using the principles of fluid dynamics. The pressure at the bottom of the tube is equal to the weight of the fluid above it, so by measuring the pressure at the bottom, the height of the fluid can be calculated.

## 5. Can fluid dynamics be applied to other areas besides glass tubes?

Yes, fluid dynamics can be applied to a wide range of systems and situations. It is used in fields such as engineering, meteorology, and oceanography to understand and predict the behavior of fluids in various environments.

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