# Total and static pressure: which one is measured?

Which pressure is measure using measuring device in a pipe flow. My first intuition that it is the static pressure. This is confirmed by this Wikipedia article (link)

The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense - they cannot be measured using an aneroid, Bourdon tube or mercury column.)

But I came across another document from MIT course (link) where the author says:

The dynamic pressure is the difference between the total pressure—that is, the pressure you would actually measure at the given point in the moving fluid, with some appropriate instrument—and the static pressure.

To the best of my knowledge the total pressure can be only measure if we bring the fluid to rest, e.g. using a pitot tube. That's why it's sometimes called stagnation pressure.

So, the question know is which quote is true? or there is a specific device that can measure the total pressure while the fluid is flowing?

Another question: in the MIT document the author says:

the dynamic pressure is zero in a stationary fluid, and also in a fluid that is in uniform motion, in the sense that there are no accelerations anywhere in the fluid (Figure 1-3).

So, why the dynamic pressure is zero in uniform flow? What is the link between dynamic pressure an acceleration? Note that in Figure 1-3 this isn't evident!!!!

• Dynamic pressure is by definition equal to $0.5\rho u^2$, so if $u\neq 0$ then dynamic pressure cannot be zero. However it is true that in a uniform flow there wouldn't be a gradient of dynamic pressure in the direction of flow. Since pressure datum is arbitrary you may pick this to be your zero pressure. – Deep Jul 19 '17 at 4:56

## 2 Answers

The dynamic pressure represents the volumic kinetic energy of the fluid, so $P_{dyn}=\frac{1}{2}\rho v^2$, and the total pressure is $P_{tot} = P_{stat} + P_{dyn}$. Thus, a device that take the speed of the fluid into account measures $P_{tot}$, and one which does not will only measure $P_{stat}$. For the first case, you can think about a Pitot tube, while for the second case you can simply use a tube which is perpendicular to the fluid flow, see this image for example.

However, one can only measure presure differences, or, in other words, when you measure a pression, you get it within a constant. Now, if the fluid is in uniform motion, $v=C^{te}$, so if you measure the total pressure, you will get $P_{mes} = P_{tot} + C^{te} = (P_{stat} + C^{te}) + C^{te}$. Finally, it is as if the dynamic pressure was zero in a stationnary fluid.

It depends on the direction of the orifice in the pressure measuring device, relative to the flow - either one can be measured. If the measuring orifice is perpendicular to the flow (such that the flow past the orifice is largely uninterrupted), then static pressure will be measured. However, if the measuring orifice is positioned in-line with the flow (such that it blocks the flow of the fluid), then it will be measuring the total pressure. This is because the measuring device blocks the flow and brings it to rest, thus converting the dynamic pressure into measurable static pressure (it is only static pressure that can actually be measured/felt).

Some pitot tubes (if you look at the Wikipedia page, for example) have orifices in both directions, which allows for the measurement of the difference between them, which gives the dynamic pressure.