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Stoke’s first problem (BSL example)

Stoke’s first problem (BSL example). Semi infinite medium: i.e. fluid extends from 0 to infinity in y direction. In the x and z directions, it extends from (minus infinity) to (plus infinity). y. x.

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Stoke’s first problem (BSL example)

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  1. Stoke’s first problem (BSL example) • Semi infinite medium: i.e. fluid extends from 0 to infinity in y direction. In the x and z directions, it extends from (minus infinity) to (plus infinity) y x • Sudden movement of plate at a constant velocity V0. The development of flow with respect to time is to be quantified • Qualitative: As time increases, you expect the ‘region of influence’ to increase; i.e. more and more fluid will be ‘aware’ of the plate movement. • Assume that if the velocity of fluid is 1% (or more) of the plate velocity V0, then we can say that the fluid is ‘aware’ of the plate movement. • Compression and expansion may move at the speed of sound in the fluid. Transfer of signal of shear stress may not.

  2. 1 Stokes First pbm • No velocity in the y or z direction • No pressure gradient • Vx does not depend on x or z • No gravity in x direction • Kinematic viscosity

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