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What is the logic behind using a wall tap/piezometer to measure the static pressure. Is it that near the walls, the fluid velocity is zero, because of the no slip condition and hence the pressure measurement near the wall would only be static pressure. There is this point in the book that i am consulting, it says "there is no pressure variation normal to straight streamlines, this fact makes it possible to measure static pressure in a flowing fluid using a wall pressure tap". Does this point mean that because there is non-variance of pressure in normal direction to the straight streamlines, thus giving a single value for static pressure, whereas in regions of curved streamlines, we would have progressively increasing values as we go away from the center of curvature of the family of curved streamlines. Also, why do we require a separate static pressure measuring instrument alongside a pitot tube (for fluids passing through a pipe) in order to measure velocity through the Bernoulli eq. Why can't we calculate velocity directly as is done, for free streams of fluids, such as river water.

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A piezometer is a device which senses pressure by producing electric signals proportional to the applied pressure. It is attached on the walls of the pipe so that the fluid pressure acts normal to it. Since the fluid flow is parallel to the walls, the fluid flow is neither obstructed by the piezometer, nor does it experience any momentum transfer. The sole force acting on the piezometer will be that caused by the hydrostatic pressure. So the need for measuring velocity of flow does not arise. This has nothing to do with no slip condition. We can place the piezometer at any point in the direction of streamline. It is more convenient to fix it on the walls.

In case of the type of gauges mentioned in your second question, they are placed normal to the flow so that they experience both hydrostatic pressure force and force due to momentum transfer(since they obstruct the flow). So we need to subtract the hydrostatic pressure to find the flow velocity.

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  • $\begingroup$ I found that the diameter is usually 12mm. Do you have any idea on the reason behind it? $\endgroup$ – Pandya Jul 15 '18 at 13:23
  • $\begingroup$ Can you explain which diameter? $\endgroup$ – Pranav Jul 15 '18 at 13:32

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