In Figure Q10 a visualization of a boundary layer over a flat plate is shown. Demonstrate using boundary layer theory, how an expression for the free stream velocity, U, of the fluid in which the plate is immersed can be estimated in terms of the boundary layer thickness, \delta, at the end of the plate. 0.0 1.0 2.0 Figure Q10: visualization of a boundary layer on a flat plate by Lee J.H. et al. The University of Melbourne.
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The boundary layer is the thin layer of fluid that forms on the surface of the plate due to the viscous effects of the fluid. It is characterized by a gradual increase in velocity from the surface of the plate to the free stream velocity. Show more…
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Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in Fig. $mathrm{P} 5.25$. This region of reduced flow is called a boundary layer. At the lcading edge of the plate, the velocity profile may be considered unformly distributed with a value $U$ All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also $U$. If the $x$ -dircction velocity profile at section (2) is [ frac{u}{U}=frac{3}{2}left(frac{y}{delta} ight)-frac{1}{2}left(frac{y}{delta} ight)^{3} ] develop an expression for the volume flowrate through the edge of the boundary layer from the leading edge to a location downstream at $x$ where the boundary layer thickness is $delta$.
Sri K.
Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in Fig. $\mathrm{P} 5.25$. This region of reduced flow is called a boundary layer. At the lcading edge of the plate, the velocity profile may be considered unformly distributed with a value $U$ All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also $U$. If the $x$ -dircction velocity profile at section (2) is \[ \frac{u}{U}=\frac{3}{2}\left(\frac{y}{\delta}\right)-\frac{1}{2}\left(\frac{y}{\delta}\right)^{3} \] develop an expression for the volume flowrate through the edge of the boundary layer from the leading edge to a location downstream at $x$ where the boundary layer thickness is $\delta$.
A horizontal surface, with length $L=0.8 \mathrm{m}$ and width $b=1.9 \mathrm{m},$ is immersed in a stream of standard air flowing at $U=5.3 \mathrm{m} / \mathrm{s}$. Assume a laminar boundary layer forms and approximate the velocity profile as linear. Plot $\delta, \delta^{*},$ and $\tau_{w}$ versus $x / L$ for the plate.
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