Pressure in piezometers with ideal fluid

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In the discussion on piezometers with ideal fluids, it is established that an inviscid fluid flowing in a horizontal pipe does not cause fluid to rise in piezometers, as the pressure remains equal to atmospheric pressure throughout. In contrast, a viscous fluid experiences a pressure drop along the pipe, allowing fluid to rise in piezometers due to the pressure gradient created by viscous drag. The pressure at points within the pipe varies, with higher pressures upstream compared to downstream, particularly in constricted sections. The conversation also clarifies that the gauge pressure in piezometers is influenced by the flow conditions and the fluid's viscosity. Overall, the application of Bernoulli's equation and the understanding of pressure dynamics in fluid flow are central to the discussion.
  • #31
fog37 said:
1) I see how a fluid at rest and a fluid in steady motion are different situations. I guess I am wondering if the isotropic pressure, at the same spatial point in the liquid, would be higher if the fluid was at rest (not a stagnation point). How different would the pressure experienced by the liquid parcels be?
Do you have a specific physical problem in mind that we can focus on (involving actual equipment and hardware)?
2) Ok, but if you take the equation in your post #29 (where ##v=0##, which implies a fluid at reset) and move the term ##\rho g z## on the righthand side, we get the equation $$P=const. - \rho g z$$, which is what I have in my post #26 (different from the correct expression for hydrostatic pressure)...
That's not what you have in post #26. You have an h instead of a z. h is measured downwards and z is measured upwards. Do you not see the difference? If the datum for both elevation and depth is taken at the upper (free) surface of the fluid, then ##h=-z## and ##p=-\rho g z = \rho g h##
 

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