A flat-plate boundary layer has profile $u/U_\infty=\sin[\pi y/(2\delta)]$, where $\delta$ is boundary-layer thickness. If displacement thickness is $\delta^*$, find $\delta^*/\delta$.
Displacement thickness is $\delta^*=\int_0^\delta(1-u/U_\infty)dy$. Substituting the profile gives $\delta^*=\delta-\int_0^\delta\sin(\pi y/(2\delta))dy=\delta-2\delta/\pi$. Thus $\delta^*/\delta=1-2/\pi$, B.
More Bernoulli's equation and fluid acceleration questions
GATE 2026 ME Q26– Bernoulli's equation CANNOT be applied between
GATE 2025 ME Q16– Consider two identical tanks with a bottom hole of diameter d. One tank is filled with…
GATE 2025 ME Q49– A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in…
GATE 2023 ME Q62– The velocity field of a certain two-dimensional flow is given by V(x, y) = k(xi - yj)…
GATE 2022 ME (ME1) Q24– A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero…
GATE 2022 ME (ME1) Q63– A steady two-dimensional flow field is specified by the stream function = kx3y, where x…