6.2. Pitot tube

Now, there is another thing pitot tube, which is used to measure the flow velocities in an aero plane as well. So, this is how a pitot tube looks like. It is used to measure air speed on aero planes. It is a very old technique but still very successfully this is used for measuring the air speed on an airplane. It can connect differential pressure transducers to measure the V square / 2g because Bernoulli equation has V square / 2g. So, what it does is measures V square / 2g and therefore tells the airspeed.

A pitot tube is a device used to measure fluid velocity, particularly in air and water. In aircraft, it measures airspeed by connecting to differential pressure sensors. The principle behind its operation is based on Bernoulli’s equation, which relates speed to pressure differences. The pitot tube takes advantage of the fact that fluid pressure changes with velocity; as fluid speed increases, static pressure decreases. Thus, the device provides a practical means of gauging airspeed by calculating the velocity head (V²/2g).

Imagine you're riding a bicycle with the wind at your back; as you pedal faster, you feel the wind against your face stronger. A pitot tube acts like your personal 'wind meter' on the bike, measuring how fast you're moving based on how strongly the air pushes against it. Just like you wouldn't be able to tell your speed without the wind, pilots rely on pitot tubes to understand how fast they're flying.

It can be used to measure the flow of water in pipelines also pitot tube. So, this is something like this, it looks something like this, in an aero plane, so this is fixed in the aeroplane. So, this shows this how many knots are there, I mean, the typical panel of the airplane speed. An important thing to note is, this is a point measurement because Bernoulli principle is applied at different points along a stream line this is important to note.

Pitot tubes can also be applied in water pipelines, measuring how swiftly water flows through them. The tube itself typically has two ports: one measuring total pressure (stagnation pressure) and one measuring the static pressure in the fluid. The difference between these two readings allows us to compute flow velocity. This 'point measurement' means the pitot tube captures data from a specific spot, and it assumes that the conditions at that spot reflect conditions along the entire streamline.

Think of a pitot tube as a thermometer measuring temperature at a specific point in a room. Just like the thermometer tells you the temperature at one spot, the pitot tube tells you the speed of the flow at that one location. While you may feel that the temperature varies across the room, the thermometer provides a crucial but limited view. Similarly, the pitot tube provides important velocity data for a specific point in a flow system, which is vital for accurate measurements.

So, pitot tube, so, there is a velocity V, there is 0.1 here and 0.2 here. So, connect 2 ports to a differential pressure transducers. Make sure that the pitot tube is completely filled with the fluid that is being measured. Solve for velocity as a function of pressure difference. This is stagnation pressure tap, this is static pressure tap. So, what it does is it measures pressure at 0.1 at 0.2. And so, the Bernoulli equation says p 1 / gamma + z 1 + V 1 square / 2g is constant. So, here, z 1 is, you know, is 0 at 0.1.

The operation of a pitot tube relies on measuring pressure differences at two points. It has a stagnation pressure tap that captures the pressure of the fluid when the velocity is zero (V=0) and a static pressure tap that measures the fluid pressure in motion. According to Bernoulli’s equation, we can relate these pressures to calculate the fluid's speed. The pressure difference effectively provides a measure of the dynamic pressure that corresponds to the flow's kinetic energy, enabling the calculation of flow velocity.

Consider how you might check the pressure in a balloon; if you pinch one side, the pressure increases on that side. Similar to this, in a pitot tube, when fluid enters, one port experiences fluid at a standstill, while the other senses fluid that's in motion. The difference in pressure helps us deduce the flow speed, just as you can infer pressure changes when handling the balloon.

We assume, that is the datum and because it is a stagnation point, the velocity at 1 will also be = 0. Because this is also at the point 2 is also here, where datum is 0, that z 2 is also = 0. So, V 1 is 0 and z 1 = z 2 that is why we have done this. So, V that is measured here is a difference of pressure and is equal to V is equal to using this equation we get this and p 1 and p 2 are measured using this pressure transducers.

When taking measurements with a pitot tube, it's often assumed that at the stagnation point (where fluid velocity is zero), the measurements of pressure correlate directly to the flow velocity. Because the pressure sensors define a reference (datum), we can express the relationship between pressures measured at both ports to determine the speed of the fluid. As a result, pitot tubes effectively simplify the determination of flow rates in various applications, from aviation to various fluid transport systems.

Imagine you're adjusting the water flow to fill a pool. To gauge how fast the water comes out of the hose, you might block the end temporarily to stop the flow, which allows you to see how much pressure builds up in the hose. This pressure, similar to what happens at the stagnation point in a pitot tube, tells you about the water flow rate once you remove the blockage. The pitot tube does this by measuring pressure differences without obstructing the flow.

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