Correct Answer - Option 1 : 0.5

__Concept:__

Nominal boundary thickness as δ

Displacement thickness is given as

\({δ ^*} = \mathop \smallint \limits_o^δ \left( {1 - \frac{u}{U_\infty}} \right)dy\)

__Calculation:__

Given, \(\frac{u}{{{u_\infty }}} = \frac{y}{\delta }\)

\({δ ^*} = \mathop \smallint \limits_o^δ \left( {1 - \frac{y }{δ}} \right)dy\)

\({δ ^*} =δ - \frac{δ }{2}\)= \(\frac{δ }{2}\)

∴ The ratio of displacement thickness to nominal thickness will be = \(\frac{{\frac{δ }{2}}}{δ }=\frac{1}{2}=0.5\)