Real-time systems (RTS) require end-to-end delay guarantees for the delivery of network packets. In this paper, we propose a framework to reduce the management and integration overheads for such real-time (RT) network flows by leveraging the capabilities of software-defined networking (SDN) - capabilities that include global visibility and management of the network. Given the specifications of flows that must meet hard real-time requirements, our framework synthesizes paths through the network. To guarantee that these flows meet both, their bandwidth and end-to-end timing requirements, our framework solves a multi-constraint optimization problem using a heuristic algorithm. We use exhaustive emulations and experiments on hardware switches to demonstrate our techniques and feasibility of our approach. As a result of this work, SDNs become 'delay-aware' and thus can be adapted for use in safety-critical and other delay-sensitive applications.