The present paper shows the influence of streamlines curvature on pressure and velocity distribution in an incompressible, non viscous, fluid motion. A radial, axially-symmetric case is analyzed. A Stokes streamfunction expansion is theoretically derived, which put into evidence the detachment of the solution from the elementary one, when the ‘shallowness’ parameter (depth scale to length scale ratio) is not vanishing. The influence of shallowness on the integral dynamical quantities, such as total linear momentum and total angular momentum, is shown, and the closure of integral mechanical balances is discussed. The behaviour of the solution at the second order is described; in any case, the method remains valid for an arbitrary requested order of accuracy. The influence of streamlines curvatures is strong in the range from 1 to 2 of the non dimensional radius, on the opposite being negligible for larger values of such a quantity.
Effects of free surface curvature on radial, inviscid flows
VALIANI, Alessandro;CALEFFI, Valerio
2003
Abstract
The present paper shows the influence of streamlines curvature on pressure and velocity distribution in an incompressible, non viscous, fluid motion. A radial, axially-symmetric case is analyzed. A Stokes streamfunction expansion is theoretically derived, which put into evidence the detachment of the solution from the elementary one, when the ‘shallowness’ parameter (depth scale to length scale ratio) is not vanishing. The influence of shallowness on the integral dynamical quantities, such as total linear momentum and total angular momentum, is shown, and the closure of integral mechanical balances is discussed. The behaviour of the solution at the second order is described; in any case, the method remains valid for an arbitrary requested order of accuracy. The influence of streamlines curvatures is strong in the range from 1 to 2 of the non dimensional radius, on the opposite being negligible for larger values of such a quantity.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
