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Some time ago I asked a question why Dynamic pressure is considered scalar.

Why is the dynamic pressure not a vector quantity?

This still puzzles me so I hope to give a scenario that doesn't make sense to me

If mass fluid flow always occurs from high pressure to low and we consider that Bernoullis tells us that Total pressure is constant along a streamline * how do we explain flow without considering the vectors of the components of that total pressure?

  • Total Pressure along a streamline of unchanging height is constant and is the sum of Static pressure and Dynamic Pressure components ?
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Quentin Chester
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  • Is there a reason you're singling out dynamic pressure in particular, or does your question apply equally to static pressure as well? – CR Drost Mar 04 '15 at 03:13
  • Hi Chris, I guess because I understand that (until the atomic scale) that static pressure is completely random (so independent of direction) thus the net force static pressure exerts on a 'parcel' of fluid is zero and does not contribute to flow .However if you think the explanation is improved by considering static pressure as by all means use this approach – Quentin Chester Mar 04 '15 at 03:21
  • Chris if you watch this video from 5:00 to 6:00 you will see that the flow is explained in form of net forces in front and behind the fluid parcel. https://www.youtube.com/watch?v=LI9Mi1KhFTs I Guess that's where I get confused as if we expand Bernoullis to Euler equations that Dynamic Pressure is also explained in the form of vectors (which I understand better than the statement that Dp does not consider vectors) – Quentin Chester Mar 04 '15 at 03:36
  • Consider something like voltage. If one part of a conductor has a higher voltage, then we expect current to flow. In simple cases like a wire knowing the voltages can immediately lead you to calculate current. But voltage is a scalar quantity with no direction, and it's current which is the vector quantity. Pressure is analogous to voltage. – MonkeysUncle Mar 04 '15 at 03:50
  • Thanks for the comment and I agree that Voltage is Scalar as if we apply the voltage perpendicular or parallel to the wire it will still flow equally in both directions along the wire. If we orient our turbine (causing the dynamic pressure) similarly perpendicular in our pipe it will cause flow in both directions but if we orientate our turbine parallel in the pipe it will cause flow in one direction only. How is this scalar ? – Quentin Chester Mar 04 '15 at 04:06
  • @QuentinChester It's a scalar because you don't need a direction to calculate it. If someone told you the density $\rho_0$ of a fluid at a particular point and they said the fluid is moving at 5m/s, you could tell them the dynamic pressure at that point because of the definition of dynamic pressure. it doesn't make sense to say "I'm sorry I can't calculate the dynamic pressure with that information because you haven't told me what direction the fluid is moving in." – MonkeysUncle Mar 04 '15 at 05:27
  • Thanks @MonkeysUncle so that's where I am going wrong. Its is not that Dynamic Pressure does not have a vector associated with it, rather Scalar only means that it is not required for a single point calculation ? – Quentin Chester Mar 04 '15 at 05:51
  • it is scalar because it is. Also, because it is isotropic, just like potential in some point creates electric field in every direction. Force, which is vector, is gradient of pressure, don't mix two up. When you create volume of excessive pressure in reservoir, liquid pushes in every direction equally. – aaaaa says reinstate Monica Mar 04 '15 at 06:08
  • @QuentinChester Well remember, if one single point can be calculated without being given a direction, every point can be calculated without being told the direction. A problem might say, "The dynamic pressure at every point in this pipe is given by $\frac{1}{2}\rho_0 \frac{x}{\sqrt{x^2+1}}$". No direction has been given, but they dynamic pressure at each point is now well defined. You have to then use other equations and boundary conditions to answer questions like "Which direction is the flow moving?" – MonkeysUncle Mar 04 '15 at 13:22
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    I really don't see how this is not still a duplicate of Define Pressure at a point. Why is it a scalar? – ACuriousMind Mar 04 '15 at 15:01

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Dynamic pressure means orderly motion. Magnitude and direction are involved. With more than one variable it becomes a vector.

Michael
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