GATE Mechanical Engineering (ME) 2016 Shift 1 Solved Paper

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is U_a. The velocity profile at the inlet a-b is uniform, while that at a downstream location c-d is given by $\mathit{u}={\mathit{U}}_0\left[2\left(\frac{\mathit{y}}{\mathit{\delta }}\right)-{\left(\frac{\mathit{y}}{\mathit{\delta }}\right)}^2\right].$

The ratio of the mass flow rate, ṁ_bd, leaving through the horizontal section b-d to that entering through the vertical section a-b is _________