How to solve a simple mercury barometer problem

Daily Dose 035 | Fluid Mechanics

How to solve a simple mercury barometer problem?

If you were asked on the FE Exam to do a pressure calculation using a simple mercury barometer, would you be able to pull it off?

Maybe?

In less than the 2’ish minutes you are given?

For most, fluid measurement isn’t at the top of the list of problem types they want to see come exam day.

If “simple” seems complicated, it’s time we tackle it head-on, reinforcing your understanding so that you can solve them with confidence – fast.

In this video, we dive into a FE Exam Practice Problem in the subject of FLUID MECHANICS, specifically, dealing with determining the pressure of a liquid using a simple mercury barometer.

Key Definition

What is a BAROMETER?

A BAROMETER is a scientific instrument used to measure ATMOSPHERIC PRESSURE, also referred to as BAROMETRIC PRESSURE.

The simplest kind of BAROMETER, which is illustrated for us in the NCEES Reference Handbook, is a tall closed tube standing upside down in a bath of mercury.

Mercury is used in BAROMETER because it’s more convenient than using water.

Water is less dense than mercury so air pressure will lift a certain volume of water much higher up a tube than the same volume of mercury.

In other words, if you use water, you need a really tall tube and your BAROMETER will be so enormous that it’d be impractical. But if you use mercury, you can get by with a much smaller piece of equipment.

We may see PRESSURE measured in mmHg, Torr, atm, psi or the typical Pascals units.

So…

The Process

How can I solve a problem using a simple mercury barometer?

Solving a simple mercury barometer problem in Fluid Mechanics typically involves the following steps:

1. Understand the problem statement: Read the problem statement carefully and make sure you understand what is being asked. Identify the given information and what you are being asked to find.
2. Draw a diagram: Draw a clear and labeled diagram of the mercury barometer, including the height of the mercury column and the atmospheric pressure acting on the exposed mercury surface.
3. Determine the density or Specific Gravity of mercury: Define the property which you will use in the hydrostatic equation.
4. Apply the hydrostatic equation: Use the hydrostatic equation found on page 179 of the NCEES FE Reference Handbook to relate the pressure difference between the top and bottom of the mercury column to the height of the column and the density of mercury.

P_atm = P_A = P_v + γh = P_B + ρgh

5. Solve for the unknown: Rearrange the hydrostatic equation to solve for the unknown pressure, height, or density as required by the problem.
6. Check your answer: Double-check your calculations and make sure your answer is reasonable and consistent with the given information.

Keep in mind that the specific steps may vary depending on the details of the problem, such as whether the mercury is in a vacuum or in contact with a fluid, or if the problem involves more than one fluid.

Check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, with Love, Prepineer

Video Review

[VIDEO] How to solve a problem using a simple mercury barometer