  Spin hydrodynamic coupling is a recently discovered method to directly
generate electricity from an electrically conducting fluid flow in the absence
of Lorentz forces. This method relies on a collective coupling of electron
spins - the internal quantum mechanical angular momentum of the electrons -
with the local vorticity of a fluid flow. In this work, we experimentally
investigate the spin hydrodynamic coupling in circular and non-circular
capillary pipe flows and extend a previously obtained range of Reynolds numbers
to smaller and larger values, 20<Re<21,500, using the conducting liquid metal
alloy GaInSn as the working liquid. In particular, we provide experimental
evidences for the linear dependence of the generated electrical voltage with
respect to the bulk flow velocity in the laminar regime of the circular pipe
flow as predicted by Matsuo et al. [Phys. Rev. B. 96, 020401 (2017)]. Moreover,
we show analytically that this behavior is universal in laminar regime
regardless of the cross-sectional shape of the pipe. Finally, the proposed
scaling law by Takahashi et al. [Nat. Phys. 12, 52 (2016)] for the generated
voltage in turbulent circular pipe flows is experimentally evaluated at
Reynolds numbers higher than in previous studies. Our results verify the
reliability of the proposed scaling law for Reynolds numbers up to Re=21,500
for which the flow is in a fully developed turbulent state.
