Bernoulli correction to viscous losses: Radial flow between two parallel discs
Flow of an inviscid fluid through a horizontal duct of changing section.
Viscous forces in a cylindrical duct. is the shear stress arising from the velocity profile v(r).
Duct defined by two plane-parallel surfaces separated by a small distance .
Radial flow between two parallel discs.
Relative pressure as a function of radial distance for (a) and (b) . Thick lines correspond to the analytical solution, including the Bernoulli correction for different values of the flow rate. Thin lines refer to the analytical solution without taking the Bernoulli correction into account. Symbols show the results obtained through numerical simulations with a finite volume method (FVM).
Deviation of the pressure change for and . The numerical simulation (empty circles) becomes unstable for less than for these particular and values. Inset: Simulated velocity profile (empty circles) compared to the parabolic profile (full circles) at (a) and (b) .
A diagram of the experimental setup. Water enters from below and flows radially to the discs boundary. The local pressure is measured through the height of the water column inside plastic hoses.
Relative pressure as a function of the radial direction for (a) and (b) cases. Lines correspond to the analytical solution including (thick) or not including (thin) the Bernoulli correction for different values of the flow rate. Symbols show the measured results. The error bars are the standard deviation of 8 (for ) and 4 measurements.
(a) Relative pressure as a function of the separation between discs at and for two flow rates. (b) Relative pressure as a function of flow rate at and for two separations between discs. Reference lines have slopes and 1, respectively.
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