For uniform laminar flow(in the $x$-direction) past a flat plate at high Reynolds number, the local boundary layer thickness ($\delta$) varies with the distance along the plate $(x)$ as

1. $\delta\propto x^{1/4}$
2. $\delta\propto x^{1/3}$
3. $\delta\propto x^{1/2}$
4. $\delta\propto x$