In this article, we demonstrate a novel microfluidic flow chamber driven by surface acoustic waves. Our device is a closed loop channel with an integrated acoustic micropump without external fluidic connections that allows for the investigation of small fluid samples in a continuous flow. The fabrication of the channels is particularly simple and uses standard milling and PDMS molding. The micropump consists of gold electrodes deposited on a piezoelectric substrate employing photolithography. We show that the pump generates a pressure-driven Poiseuille flow, investigate the acoustic actuation mechanism, characterize the flow profile for different channel geometries, and evaluate the driving pressure, efficiency and response time of the acoustic micropump. The fast response time of our pump permits the generation of non-stationary flows. To demonstrate the versatility of the device, we have pumped a red blood cell suspension at a physiological rate of 60 beats/min.