The mathematical modeling of particulate flows naturally lead to systems of conservation laws involving constraints on velocity fields. The numerical treatment of the constrained systems of PDEs might lead to difficulties: it is not clear that different formulations of the equations remain equivalent at the discrete level, and a careless approach might give rise to spurious instabilities, or to unsatisfactory mass and energy balances. This is reminiscent to the difficulties that appear in the simulation of Euler equations in low Mach regimes, when using standard Riemann solvers. We introduce a new class of schemes for the Euler equations that work on staggered grids, numerical densities and velocities being stored in different locations. Moreover, the design of the numerical fluxes is inspired from the principles of the kinetic schemes. Stability conditions ensuring the positivity of the discrete density and energy can be identified, for both first and second order version of the scheme. The method can be incorporated into a suitable splitting strategy to handle low Mach simulations.