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Consider the boundary-layer flow in the immediate neighbourhood of the separation point x = x, where r, is zero. Show that 7 x (x,-x)2 when x is T a u close to x,, provided that- (x,,0) is finite and non-zero. (Note: Due to the ay¹ Tw rapid change in the skin-friction and other variables, accuracy is lost in numerical computations. This is often called the problem of Goldstein's singularity. This square-root singularity is a consequence of treating the mainstream pressure gradient dP/dx as a prescribed quantity.)

Consider the boundary-layer flow in the immediate neighbourhood of the separation point x = x, where r, is zero. Show that 7 x (x,-x)2 when x is T a u close to x,, provided that- (x,,0) is finite and non-zero. (Note: Due to the ay¹ Tw rapid change in the skin-friction and other variables, accuracy is lost in numerical computations. This is often called the problem of Goldstein's singularity. This square-root singularity is a consequence of treating the mainstream pressure gradient dP/dx as a prescribed quantity.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Consider the boundary-layer flow in the immediate neighbourhood of the separation point x x, where T, is zero. Show that 7, (x,– x)"² when x is ciose to x,, provided that a* u (x,%) is finite and non-zero. (Note: Due to the 4 rapid change in the skin-friction and other variables, accuracy is lost in numerical computations. This is often called the problem of Goldstein's singularity. This square-root singularity is a consequence of treating the mainstream pressure gradient dP/dx as a prescribed quantity.)
Transcribed Image Text:7. Consider the boundary-layer flow in the immediate neighbourhood of the separation point x x, where T, is zero. Show that 7, (x,– x)"² when x is ciose to x,, provided that a* u (x,%) is finite and non-zero. (Note: Due to the 4 rapid change in the skin-friction and other variables, accuracy is lost in numerical computations. This is often called the problem of Goldstein's singularity. This square-root singularity is a consequence of treating the mainstream pressure gradient dP/dx as a prescribed quantity.)
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