# The Pitot Tube

Topics: Fluid dynamics, Stagnation pressure, Mass flow rate Pages: 11 (1799 words) Published: February 23, 2013
INTRODUCTION

Nowadays, a Pitot tube would be of use as a speedometer on aeroplanes. It is also found useful in industries where velocity measurements are required, where an anemometer may not be the most efficient instrument to use. There are three types of pitot tubes: Pitot tubes, Static tubes, and Pitot-Static tubes.

The simple pitot tube essentially consists of a tube bent at - usually - 90°, with an open end pointing directly towards the fluid flow. As the fluid flows in the tube, it becomes stagnant since there is no direct opening at the other end for it to exit from. As the inert fluid rises, it creates a pressure of its own. This pressure is equivalent to the dynamic pressure, which can be seen as the kinetic energy of the fluid per unit weight.

F.X. Pitot originally used this device to analyze the pressure created by the stagnating fluid at the other end of the tube. He did this by calculating the sum of the dynamic pressure and static pressure. The pressure created by the stagnant fluid (stagnation pressure) is found where the velocity component is zero. Using these principles, it is possible to determine a fluids velocity.

This has manifested itself in the form of the Bernoulli equation. It describes this phenomenon as it states that an inviscid fluid’s increase in velocity is accompanied with a concurrent decrease in pressure or in the fluid's potential energy. However, this equation works on two assumptions – the first, that the fluid is incompressible; the second, that friction caused by viscous forces are to be considered negligible. The Bernoulli equation can nevertheless be used for compressible flows, but only at low Mach numbers.

In the experiment, we measured the radial velocity profile at a cross-section of a pipe using the Pitot tube. As the Pitot probe is shifted along the pipe, we can record the stagnation pressure and static pressure at that cross-section of the pipe. The velocity of the inviscid fluid can now be found using both pressures.

The smaller the diameter of the Pitot tube is, the more accurate the flow velocity. If the Pitot tube has too large a diameter, results for the fluid’s flow could be inaccurate due to the difference in velocity between the fluid against the tube walls and the fluid in the middle of the tube.

Background and Theory

One of the most fundamental equations in the field of fluid mechanics is the Bernoulli Equation:

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As stated in the introduction, this equation is based on the assumption that the density and velocity of the fluid are constant.

If we then multiply both sides of the Bernoulli equation (eq.1) by the denominator density ([pic]), the result is:

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We can assume, for the Venturi tube, that [pic], as it is placed on a horizontal surface and therefore does not change height. This means that height stays constant. Subsequently, eq. 2 can be rephrased into:

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At this point, a number of things can be done to the Bernoulli equation. It is possible to make use of the relationship found in the Continuity equation, which states that the volumetric flow rate [pic] – the volume of fluid passing a point in the system, per unit time - is equal to the product of the cross-sectional area (A) and the average flow of velocity (v):

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The substitution is performed as such, and the new equation can be rearranged with respect to [pic]:

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Here, we can benefit from the basic equation relating volumes (V), mass (m) and density ([pic]:

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By dividing by time (t) both sides of equation (eq. 6) by end up with:

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and therefore:

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([pic]) = Mass Flow Rate

If we now substitute eq. 6b into eq. 5, the outcome becomes:

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Pitot tubes are used to calculate pressure at a certain point. To do this, two points are selected inside the airflow –...