We give the closed form solutions to the parallel time and speedup of the classic method for processing divisible loads on linear arrays as functions of {\rm N}, the network size. We propose two methods which employ pipelined communications to distribute divisible loads on linear arrays. We derive the closed form solutions to the parallel time and speedup for both methods and show that the asymptotic speedup of both methods is \beta + 1, where \beta is the ratio of the time for computing a unit load to the time for communicating a unit load. Such performance is even better than that of the known methods on \kappa-dimensional meshes with \kappa gt; 1. The two new algorithms which use pipelined communications are generalized to distribute divisible loads on \kappa-dimensional meshes, and we show that the asymptotic speedup of both algorithms is \kappa \beta + 1, where \kappa \geqslant 1. We also prove that on \kappa-dimensional meshes where \kappa \geqslant 1, as the network size becomes large, the asymptotic speedup of 2\kappa \beta + 1 can be achieved for processing divisible loads by using interior initial processors.