string sourceFileName = "source.txt";
            string destinationFileName = "File-Part-{0}.txt";
            int linesPerFile = 3;

            using (var sourceFile = new StreamReader(sourceFileName))
            {
                var fileCounter = 0;
                var destinationFile = new StreamWriter(
                    string.Format(destinationFileName, fileCounter + 1));

                try
                {
                    var lineCounter = 0;

                    string line;
                    while ((line = sourceFile.ReadLine()) != null)
                    {
                        if (lineCounter >= linesPerFile)
                        {
                            lineCounter = 0;
                            fileCounter++;

                            destinationFile.Dispose();
                            destinationFile = new StreamWriter(
                                string.Format(destinationFileName, fileCounter + 1));
                        }

                        destinationFile.WriteLine(line);
                        lineCounter++;
                    }
                }
                finally
                {
                    destinationFile.Dispose();
                }
            }