The Reynolds number, $R e$ is defined as $\frac{U_{\infty} L}{v}$ where $L$ is the length scale for a flow, $U_{\infty}$ is its reference velocity and $v$ is the coefficient of kinematic viscosity. In the laminar boundary layer approximation, comparison of the dimensions of the convection term $u \frac{\partial u}{\partial x}$ and the viscous term v $\frac{\partial^{2} u}{\partial x^{2}}$ leads to the following relation between the boundary layer thickness $\delta$ and $R e$ :
(A) $\delta \propto \sqrt{R e}$
(B) $\delta \propto 1 / \sqrt{R e}$
(C) $\delta \propto R e$
(D) $\delta \propto 1 / R e$

Question ID - 155717 | SaraNextGen Top Answer

The Reynolds number, $R e$ is defined as $\frac{U_{\infty} L}{v}$ where $L$ is the length scale for a flow, $U_{\infty}$ is its reference velocity and $v$ is the coefficient of kinematic viscosity. In the laminar boundary layer approximation, comparison of the dimensions of the convection term $u \frac{\partial u}{\partial x}$ and the viscous term v $\frac{\partial^{2} u}{\partial x^{2}}$ leads to the following relation between the boundary layer thickness $\delta$ and $R e$ :
(A) $\delta \propto \sqrt{R e}$
(B) $\delta \propto 1 / \sqrt{R e}$
(C) $\delta \propto R e$
(D) $\delta \propto 1 / R e$