Question

Air flows steadily at velocity $V = 90$ m/s over a smooth flat plate of length $L = 18$ m. Given the air kinematic viscosity is $v = 1.52 \times 10^{-5}$ m$^2$/s. Assuming that the boundary layer is fully turbulent from the beginning of the plate and the boundary layer profile can be estimated by the one-seventh-power law, defined as: $\frac{u}{V} = (\frac{y}{\delta})^{1/7}$ i. Complete Table 2.1 by calculating the velocity $u$ at various distance $y$ from the wall at $x = L$. ii. Plot the turbulent boundary layer profile in physical variables ($u$ is the horizontal axis and $y$ is the vertical axis) y, mm 0.0 5.0 10.0 20.0 30.0 40.0 50.0 100.0 150.0 250.0 u, m/s 0 142.04 156.83 173.15 183.48 191.17 197.37 217.91 230.91 268.39 turbulent # (18 marks) (b) For the boundary layer profile of Q2(a) above, determine: i. The displacement thickness in term of boundary layer thickness $\delta$. ii. The momentum thickness in term of boundary layer thickness $\delta$.

          Air flows steadily at velocity $V = 90$ m/s over a smooth flat plate of length $L = 18$ m. Given the air kinematic viscosity is $v = 1.52 \times 10^{-5}$ m$^2$/s. Assuming that the boundary layer is fully turbulent from the beginning of the plate and the boundary layer profile can be estimated by the one-seventh-power law, defined as:

$\frac{u}{V} = (\frac{y}{\delta})^{1/7}$

i. Complete Table 2.1 by calculating the velocity $u$ at various distance $y$ from the wall at $x = L$.
ii. Plot the turbulent boundary layer profile in physical variables ($u$ is the horizontal axis and $y$ is the vertical axis)

y, mm	0.0	5.0	10.0	20.0	30.0	40.0	50.0	100.0	150.0	250.0
u, m/s	0	142.04	156.83	173.15	183.48	191.17	197.37	217.91	230.91	268.39

turbulent #
(18 marks)
(b) For the boundary layer profile of Q2(a) above, determine:
i. The displacement thickness in term of boundary layer thickness $\delta$.
ii. The momentum thickness in term of boundary layer thickness $\delta$.

Added by Summer N.

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