Daily Dose 044 | Fluid Mechanics
How to use a Manometer to find Pressure Difference?
When it comes down to taking the FE Exam, you can count on needing to know how to use a Manometer to find Pressure Differences.
These problem types, found within the Fluid Mechanics portion of the exam, tend to work around one of three manometer types:
- Single Column Manometer
- U-tube manometer
In this video, we dive into part 1 of an FE Exam Practice Problem on the subject of FLUID MECHANICS OF LIQUIDS, showing you how to quickly and efficiently find the pressure difference using a manometer.
What is a MANOMETER?
A MANOMETER is a scientific instrument used to measure PRESSURES.
The most common MANOMETER consists of a U-shaped glass tube filled with some high-density liquid (typically mercury). This type of MANOMETER is represented in your NCEES REFERENCE HANDBOOK.
Generally speaking, when in use, the U-TUBE MANOMETER is installed in an upright position.
When exposed to the same pressure on both ends, the levels of the fluid in the two vertical columns will be equal, this is referred to as the ZERO POINT of the MANOMETER.
The MANOMETER is placed against a measuring scale to allow any difference in the height of the two columns to be noted. This height differential can be used directly to make relative comparisons between different test PRESSURES.
So how can we use a manometer to find Pressure Difference?
You can quickly and efficiently find the pressure difference using a manometer in any Fluid Mechanics problem you get on the FE Exam following these steps:
- Understand the problem
- Identify the reference point
- Determine the fluid properties
- Analyze the manometer configuration
- Apply the appropriate equation
- ΔP is the pressure difference
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height difference between the fluid levels in the two arms of the manometer
- Θ is the inclined angle of the manometer
- Perform the calculations
- Verify the direction of pressure difference
Read the problem statement carefully and make sure you understand the scenario and what is being asked. Identify the fluids or gases that are involved, their properties, and the specific configuration of the manometer.
Determine the reference point for measuring the pressure difference. In a manometer, the reference point is typically an open or closed end exposed to atmospheric pressure. This will be the point where the pressure is known or given.
Identify the properties of the fluids or gases in the manometer. These properties may include densities, specific gravities, or any other relevant information provided throughout the problem statement.
Examine the specific configuration of the manometer in the problem. There are different types of manometers, such as U-tube, inclined, or differential manometers. Understand how the fluids or gases are connected and the positions of the reference and unknown points.
Depending on the manometer type and configuration, you will use different equations to calculate the pressure difference, all of which can be referenced in the FE Reference Handbook.
For a U-tube manometer, the pressure difference can be determined using the equation:
ΔP = ρgh
For an inclined manometer, The pressure difference can be calculated using trigonometry and the equation:
ΔP = ρghsinΘ
For a differential manometer, the pressure difference can be determined by comparing the height differences between the two arms of the manometer, using the equation:
ΔP = ρgh
Substitute the known values from the problem statement into the appropriate equation and calculate the pressure difference.
Consider the relative positions of the fluid or gas columns in the manometer. The pressure difference may be positive or negative depending on whether the unknown point is higher or lower than the reference point. Make sure to interpret the direction correctly based on the problem statement.
Check out the video and see how we can go about solving this type of problem in the most efficient manner.
We are here to help.
As always, with Love, Prepineer
[VIDEO] How to use a Manometer to find Pressure Difference
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