  Carpets under consideration here, in the context of pressure acoustic waves
propagating in a compressible fluid, do not touch the ground: they levitate in
mid-air (or float in mid-water), which leads to approximate cloaking for an
object hidden underneath, or touching either sides of a square cylinder on, or
over, the ground. The tentlike carpets attached to the sides of a square
cylinder illustrate how the notion of a carpet on a wall naturally generalizes
to sides of other small compact objects. We then extend the concept of flying
carpets to circular cylinders. However, instead of reducing its scattering
cross-section like in acoustic cloaks, we rather mimic that of another
obstacle, say a square rigid cylinder. For instance, show that one can hide any
type of defects under such circular carpets, and yet they still scatter waves
just like a smaller cylinder on its own. Interestingly, all these carpets are
described by non-singular acoustic parameters. To exemplify this important
aspect, we propose a multi-layered carpet consisting of isotropic homogeneous
fluids with constant bulk modulus and varying density which works over a finite
range of wavelengths. We have discussed some applications, with the sonar boats
or radars cases as typical examples. For instance, we would like to render a
pipeline lying on the bottom of the sea or floating in mid-water undetectable
for a boat with a sonar at rest just above it on the surface of the sea.
Another possible application would be protecting parabolic antennas.
