  The role of intrinsic $k_\perp$ in semi-inclusive Deep Inelastic Scattering
(SIDIS) processes ($l p \to l h X$) is studied with exact kinematics within QCD
parton model at leading order; the dependence of the unpolarized cross section
on the azimuthal angle between the leptonic and the hadron production planes
(Cahn effect) is compared with data and used to estimate the average values of
$k_\perp$ both in quark distribution and fragmentation functions. The resulting
picture is applied to the description of the weighted single spin asymmetry
$A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES
collaboration at DESY; this allows to extract parameters for the quark Sivers
functions. The extracted Sivers functions give predictions for the COMPASS
measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent
data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed
and found to be small. Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for
kaon production at HERMES are also given.
