A smooth ceramic sphere $($SG $=2\mathrm{.}6)$ is immersed in a flow of water at $20$C and $1$ cm$/$s$.$

What is the sphere diameter $($in micrometer$)$ if it is encountering creeping motion, Red $=1?$

$$ x$=0\mathrm{.}16$Re$1/7$xx$=0\mathrm{.}16$Rex$1/7$

Devise a scheme for determining the boundary layer thickness more accurately when the flow is laminar up to a point Rex,crit and turbulent thereafter. Apply this scheme to compute the boundary layer thickness at x $=1\mathrm{.}5$ m in $48$ m$/$s flow of air at $20$C and $1$ atm past a flat plate. Compare your result with the equation and determine the change in the boundary layer thickness. Assume Rex,crit $<1\mathrm{.}2$ E$6.$

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The boundary layer thickness is m$.$

When compared with a straight all$-$turbulent$-$flow calculation $($using the given relation$),$ the boundary layer thickness is m$.$