# Pitot Tube

by Jared Rovny

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00:01 The question now and this is the last part is how could we possibly experimentally find the fluid flow in a given pipe. So, suppose we have some pipe and we have fluid flowing through it like this one, what can we do to measure the flow in this pipe? First of all, let’s introduce a definition which is that the pressure plus the term that comes from the kinetic energy, the pressure plus ½ ρv squared is sometimes called the static pressure of a fluid. So, we’re going to use that to our benefit. This is called a pitot tube. We’re able to use it to measure the velocity of the fluid flow in a given pipe. What we do is insert this into a pipe and have some sort of measuring device above it which I’ll discuss in a second. It has two types of openings.

00:48 You see that it has a horizontal opening where fluid would try to flow into this blue area as I’ve shaded it.

00:54 It also has thinner, smaller openings which I’ve shaded in green here. So, you can see that there’s a difference between these two kinds of openings. The important thing here is that at the end of this pitot tube, right at the top of it, we’ve closed it off. There’s not going to be any fluid flowing actually through the pitot tube. It actually is closed off so that the fluid flow through it is nonexistent. There's no actual motion of water. So for example, in this blue area and in the green area, neither of these fluids are moving in the light blue and the green area even though the fluid in your pipe as a whole, which is represented in dark blue, is moving.

01:30 What this means is that the motion of the fluid past the green area is going to go just right past the opening of the pitot tube that goes downwards. So, this velocity of fluid will go right past it.

01:46 You will not measure the kinetic energy part of your pressure equation. So, look at this pressure equation, P plus ½ ρv squared. This ½ ρv squared term will not be measured by your pitot tube in this green section because it’s only measuring the pressure to the side of the flow perpendicular to the direction of the flow just like when we were talking about the pressure rising in a pipe that’s having to fight gravity. That height was only measuring the pressure and not the pressure from the fluid flow. On the other hand, this part of the pitot tube that’s going directly into your current, even though that fluid isn’t moving, the lighter blue fluid inside your pitot tube, it does have the velocity of the water impacting it. As that velocity of the water impacts it, it gets not only the normal pressure of the water, it’s also experiencing the hits from the velocity of the water as it impacts the side of the column of water in the pitot tube. So, the total pressure in this part of the pitot tube will be greater because of the contribution from the velocity term.

02:48 So, this part of the pitot tube gets the full static pressure. All we have to do now to measure this is hook this up to an apparatus which can measure the difference in pressures between the green and the blue. For example, we can put a membrane or something in between the two and measure the displacement of the membrane as it's pushed to one side or the other because one of these pressures is greater than or less than the other pressure.

03:11 By measuring the difference in these pressures, we can solve the equation that we have written here for the static pressure for the velocity of the water. So if we rearrange, we see that the velocity of the water is simply related to a few variables that we can measure using our pitot tube.

03:27 We know the density of our fluid. We could know that a priori by knowing what fluid we were talking about.

03:33 The pitot tube in the apparatus above it will help us to measure the difference in the static pressure and the pressure without the velocity term. So long as we know that term, we can solve for the velocity.

03:43 Pitot tubes are used for this reason to find the velocity of fluid flowing in many systems.

### About the Lecture

The lecture Pitot Tube by Jared Rovny is from the course Fluids.

### Included Quiz Questions

1. The speed of the flowing fluid, using the difference between the total and static pressure measured by the Pitot tube
2. The density of the fluid
3. The total pressure, by knowing the static pressure and the speed of the fluid measured by the Pitot tube
4. Only the static pressure of the fluid is measured by a Pitot tube
5. Only the total pressure of the fluid is measured by a Pitot tube
1. The total pressure P_t = P + 1/2 ρv² and static pressure P_s = P are measured using 2 different tubes related to the Pitot tube and the difference P_t - P_s = 1/2 ρv² ≡ P_d is used to determine the dynamic pressure P_d and hence the speed of the fluid. "P" is the static pressure, while 1/2 ρv^2 is the dynamic pressure. The sum of dynamic and static pressure is the total pressure.
2. Using a speedometer that is attached to the Pitot tube
3. The kinetic energy of a portion of the fluid is measured by determining the maximum height which this fluid jumps in a tube. This measured kinetic energy is then used to determine the speed of the fluid.
4. A fairly complex system of tubes is used to determine the dynamic pressure P_d = 1/2 ρv^2 directly. With knowing P_d the speed of the fluid is determined easily.
5. Pitot tube is mainly used to measure the static pressure of the fluid.
1. P_t can never be less than P_s, because the dynamic pressure is always greater than or equal to zero.
2. The speed would acquire a minus sign, indicating flow in the opposite direction.
3. The speed of the fluid becomes an imaginary number, indicating flow has become turbulent.
4. The speed of the fluid in this case cannot be determined using this equation and more advanced calculations are needed.
5. In this case the absolute value of the difference is considered in order to keep the expression under the square root positive.

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