"The flow coefficient is Q/sqrt(dP), a volumetric flow/sqrt(pressure)."

The units, specifically, are:

Kv = (m3/h)/sqrt(bar)
Cv = (usgal/min)/sqrt(psi)

Repasted from the omitted text:

"The only way I can think of to do it is to make a system with the
components within the derived dimension and make conversion factors for
those.  The problem is that I am not sure such systems can be coherent
and it would be a significant effort above and beyond the direct
conversion factors I already know."

To finish the thought, you can get a function to take any quantity of volumetric flow/sqrt(pressure) as follows (using the previous code) :

namespace boost {
namespace units {

typedef 
make_dimension_list< list< dim< length_base_dimension,static_rational<7,2> >,
                     list< dim< mass_base_dimension,static_rational<-1,2> >, dimensionless_type > > >::type funky_type;

} // namespace units 
} // namespace boost

using namespace boost::units;

template<class Y,class System>
void f2(const quantity<unit<funky_type,System>,Y>& arg)
{
std::cout << quantity<Kv,Y>(arg) << std::endl;
}

int main(void)
{
f2(1.0*Kv());
f2(1.0*Cv());
}

Matthias