Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. a) Is the flow field incompressible at all times? b) Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt. c) By considering the velocity gradients, determine whether the fluid elements experience any deformation. What type(s) of deformation do they experience? d) Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.
Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. a) Is the flow field incompressible at all times? b) Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt. c) By considering the velocity gradients, determine whether the fluid elements experience any deformation. What type(s) of deformation do they experience? d) Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:1.
Consider a two-dimensional flow which varies in time and is defined by
the velocity field, u= 1 and v = 2yt.
a) Is the flow field incompressible at all times?
b) Compute the convective derivative of each velocity component: Du/Dt
and Dv/Dt.
c) By considering the velocity gradients, determine whether the fluid
elements experience any deformation. What type(s) of deformation do
they experience?
d) Do the fluid elements experience angular rotation? Thus, state whether
the flow field is rotational or irrotational.
e) Given that the density of the fluid does not vary spatially and changes
only with time, what differential equation for the density, p(t), must be
satisfied for this scenario to represent a physical, compressible flow
field?
f) At time t = 0, the density everywhere is p = po. Determine how the
density changes with time, given the situation does represent a
physical, compressible flow field.
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