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On the unsteady unidirectional flows due to sudden application of a pressure gradient

Erdogan M. E.

International Journal of Applied Mechanics and Engineering

2001

Vol. 6, no 2

345-368

Some properties of unsteady unidirectional flows of viscous fluids are discussed for flows impulsively started from rest by a constant pressure gradient in the direction of the flow. Three illustrative examples are given. The first example is the unsteady Poiseuille flow, the second is the unsteady generalized Couette flow and the third is the unsteady flow in a circular pipe. It is found that the expressions of the quantities such as velocity, flux and skin friction are in series forms which may be rapidly convergent for large values of the dimensionless time but slowly convergent for small values of the dimensionless time or vice versa. It is shown that if their expressions can be found for one of large values of the dimensionless time or small values of the dimensionless time, these expressions can also be used for the other.