A vortex generator in the shape of a low aspect-ratio
wing is located on the wing of a Boeing 707. The height
of the vortex generator is comparable to the thickness
of the turbulent boundary layer over the wing. Give a
qualitative description of the effect of the vortex
generator on the momentum transfer in the boundary
layer. A fully developed turbulent pipe flow of fluid with a
Prandtl number equal to one is being cooled by the
addition of a small volume of slightly cooler fluid
over the cross section. Estimate the initial temperature
fluctuation level. How many pipe diameters downstream are
required before the temperature fluctuations have
decayed to 1% of the initial level? For the purpose of
this calculation, it may be assumed that the mean
velocity in the pipe is approximately independent of
position. Also, an estimate for the dissipation rate,
e, is needed; it can be obtained from the momentum and
energy integrals for pipe flow. For a prescribed
decrease in mean temperature in the pipe, should one
increase the volume flow of coolant and reduce the
temperature difference or vice versa to reduce the
temperature fluctuation?
wing is located on the wing of a Boeing 707. The height
of the vortex generator is comparable to the thickness
of the turbulent boundary layer over the wing. Give a
qualitative description of the effect of the vortex
generator on the momentum transfer in the boundary
layer. A fully developed turbulent pipe flow of fluid with a
Prandtl number equal to one is being cooled by the
addition of a small volume of slightly cooler fluid
over the cross section. Estimate the initial temperature
fluctuation level. How many pipe diameters downstream are
required before the temperature fluctuations have
decayed to 1% of the initial level? For the purpose of
this calculation, it may be assumed that the mean
velocity in the pipe is approximately independent of
position. Also, an estimate for the dissipation rate,
e, is needed; it can be obtained from the momentum and
energy integrals for pipe flow. For a prescribed
decrease in mean temperature in the pipe, should one
increase the volume flow of coolant and reduce the
temperature difference or vice versa to reduce the
temperature fluctuation?
