How do you find fluid velocity using a Pitot Tube

Daily Dose 017 | Fluid Mechanics

How do you find fluid velocity using a Pitot tube?

Finding the fluid velocity using a Pitot tube is one of those gray area problem types that we would rather not see on our FE Exam.

Diving in to the components of FLUIDS (figuratively of course) can get quite complex and even more so when we start navigating in the realm of fluid flow measurement.

But it doesn’t need to be complex, in this lesson, we dive in to an FE Exam Practice Problem in the subject of FLUID MECHANICS, specifically revolving around defining the FLUID VELOCITY using a PITOT TUBE.

Key Definition

What is a PITOT TUBE?

A PITOT TUBE is a pressure measurement instrument used to measure fluid flow velocity.

As engineers, we see PITOT TUBES used to determine the airspeed of an aircraft, water speed of a boat, and to measure liquid, air and gas flow velocities.

In the problem that we will get into, a PITOT TUBE used to measure the local flow velocity at a given point in the flow stream.

The basic PITOT TUBE consists of a tube pointing directly into the flow of a fluid. As this tube contains fluid, a pressure can be measured; the moving fluid is brought to rest as there is no outlet to allow flow to continue.

This pressure is the stagnation pressure of the fluid, also known as the total pressure or (particularly in aviation) the pitot pressure.

The Process

What is the process of using a Pitot Tube?

At its core, the Pitot Tube is a fairly simple, yet profoundly effective instrument.

It allows for us, through the comparison of a few specific pressures, to determine the velocity of the fluid.

Knowing the velocity of a fluid is essential for safety, design efficiency, and environmental considerations in engineering and science.

For instance, in aviation, it’s crucial to determine airspeed to prevent flight hazards.

In hydraulic systems, fluid velocity dictates the design and operation of pumps and valves.

In environmental contexts, water velocity in treatment plants can influence pollutant removal.

Whether we are optimizing a process, ensuring safety, or abiding regulations, understanding fluid velocity plays a pivotal role, and for this reason, we are likely to see a problem on our FE Exam asking us to determine a fluid velocity using a Pitot tube.

The following procedure gives you a general framework to determine the fluid velocity using a Pitot tube fast and efficiently no matter how complex of a scenario you are presented.

Let’s run through the steps:

1. Locate the formulas in the NCEES FE Reference Handbook

Currently, you can find information in regards to the Pitot tube on page 195 of the NCEES FE Reference Handbook, which gives us:



We are given both a general formula as well as a schematic to visualize how the tool is being implemented and what data we are after to properly determine the variable we are after.

You must understand that a Pitot tube will allow you to measure the stagnation pressure (or total pressure) at the inlet of the tube, and will often be used in conjunction with a static port that measures the static pressure of the fluid.

2. Define the Stagnation (or Total) Pressure (P₀)

Reading through the problem statement (or looking over the diagram given) define the Stagnation (Total) Pressure. This is the pressure measured at the inlet of the Pitot tube.

3. Determine Static Pressure (P_s)

Reading through the problem statement (or looking over the diagram given) define the Static Pressure. This is the pressure of the fluid measured at a port that is perpendicular to the flow direction, and at a point where the fluid is at rest, ensuring that the fluid’s motion doesn’t impact the measurement.

4. Determine the fluids density, ρ (or specific gravity, γ)

Reading through the problem statement (or looking over the diagram given) define the density or specific gravity of the fluid being measured.

In some cases, you may need to reference the fluid property tables for water at the end of the Fluid Mechanics section in the NCEES FE Reference Handbook.

5. Solve for the Fluid Velocity

Using the formula:

• v = √(2/ρ)(P₀ – P_s) or,
• v = √(2g)(P₀ – P_s)/γ

Where:

• v = Velocity of the Fluid
• P₀ = Stagnation Pressure
• P_s = Static Pressure of the fluid where the elevation that the measurement is taken
• ρ = Density of the Fluid
• γ = Specific Gravity of the Fluid
• g = Gravity

Plug in all the data gathered to determine the fluid velocity using a Pitot tube.

6. Considerations and Corrections

There may be a problem on your FE Exam that requires you to consider things that may affect the accuracy of the fluid measurement made using the Pitot tube. In this case, here are a few key considerations:

• Ensure the Pitot tube is aligned with the flow to get accurate readings.
• Calibrations or corrections may be required depending on the fluid properties, the geometry of the flow field, and the type of Pitot tube being used.
• The provided formula assumes incompressible flow. For compressible flows (like high-speed air flows), the relationship between velocity and dynamic pressure becomes more complex, requiring additional considerations.

Following these general steps will ensure you can confidently calculate the velocity of fluid flow in various engineering applications.

And with all of that being stated, check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, we are here to help, Prepineer

Video Review

[VIDEO] How to find fluid velocity using a Pitot tube