GATE 2016 ME (ME1) – Question 51
A steady laminar boundary layer forms over a flat plate as shown. The free-stream velocity is $U_0$. The inlet profile at a–b is uniform; downstream at c–d, $u=U_0[2(y/\delta)-(y/\delta)^2]$. The ratio of mass flow leaving through horizontal b–d to that entering through vertical a–b is ______.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.32 to 0.34
Explanation
Per unit width, inlet mass flow isρU0δ. Downstream flow isρU0δ∫0¹(2η−η²)dη=(2/3)ρU0δ. With no wall penetration, continuity sends the difference through b–d. Its inlet-flow fraction is1−2/3=**1/3**, approximately0.3333.