Modifying the file 0/U the /incompressible/icoFoam/cavity tutorial.

FoamFile
{
version 2.0;
format ascii;
class volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions [0 1 -1 0 0 0 0];

internalField uniform (0 0 0);

boundaryField
{
movingWall
{
type codedFixedValue;
value $internalField;
redirectType ramp;
code
#{
scalar U_0=0.049954; //mean U.This isn't the max velocity of the profile.
scalar r=0.05; //mean Radius. in the 3 pipes radius are different.
fixedValueFvPatchVectorField myPatch(*this);
forAll(this->patch().Cf(),i)
{
myPatch[i]=vector(2*U_0*(1-Foam :: pow(this->patch().Cf()[i].x()-0.05,2)/Foam :: pow(r,2)),0,0);
}
operator==(myPatch);
#};
}

fixedWalls
{
type fixedValue;
value uniform (0 0 0);
}

frontAndBack
{
type empty;
}
}

then icoFoam ...
boundary condition is then calculated at 0 and duplicated at other time steps.

May need