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In this paper, we present a dynamic load-balancing scheme in a networked heterogeneous computing environment and apply it to a Web-based scientific visualization system, whose efficiency requires a much stronger support than what is needed for visualizations merely on a single computer. To achieve the overall system resource utilization and to determine the most cost-effective strategy for such computing applications, we adopt a distributed asynchronous pipeline approach and a dynamic load-balancing algorithm at server side to distribute tasks among the whole system. To achieve efficient pipelining, it essentially requires a network with high bandwidth and low latency; an efficient interprocess communication mechanism on the network, and proper adaptation and partitioning of the visualization computations through the pipeline. By taking each client's capability into consideration, this dynamic approach can dispatch some stages of the visualization pipeline to client for executing. Besides, we also present a mechanism for selecting a computing unit that best suits for executing a specific visualization computation in the incoming job. We have demonstrated a number of static and dynamic configurations in task allocation and functional partitioning in order to realize the target application.