Due to increasing demands for faster and faster manufacturing of new complex materials, such as casting of particulate composites, the determination of pumping pressures needed for particle-laden fluids through channels is critical. In particular, the increase in viscosity as a function of the particle volume fraction can lead to system malfunction, due to an inability to deliver necessary pressures to pump the more viscous fluid through the system. This paper studies the pressure gradient needed to maintain a given flow rate, explicitly as a function of the volume fraction of particles present in the fluid. It is also crucial to control voids in the casted products, which can be traced to air-entrainment, spurious internal reactions, dewetting, etc., which can be traced to high Reynolds numbers. Accordingly, an expression for the resulting Reynolds number as a function of the particle volume fraction and flow rate is also developed. Numerical examples are provided to illustrate the practical use of the derived relations to characterize the necessary pumping pressures for process-driven, particle-laden fluid flows.