DAL Controller described a departure overtake loss of separation event when a HS25 overtook a previous B727 aircraft; noting a D10 Controller was less than helpful in providing a relief heading approvals.

Narrative

[I was] working Local Control West position and one runway operation. Departed a B727 followed by a HS25. The B727 was super slow (140 KTS) and the HS25 was super fast on departure climb-out (220 KTS). I saw the problem and tried to correct by telling the HS25 to maintain 3;000 FT altitude; as my Coordinator tried to effect a turn with Dallas South. Dallas South said unable turn; he was asked twice for two different headings. He did not appear to have any traffic in the direction in which we wanted to go. Then I coordinated with the Departure Controller 1 and asked for a heading in the same direction as we just asked the other South Controller; and it was approved! Guess it depends on who you ask! So then I turned the HS25 to the south; and switched the HS25 to departure. Recommendation; we will not launching the second aircraft so close to the first; would be my first; but I had to launch him because I had a B737 coming in for that runway; and the HS25 was on the runway. But the Dallas South Controller could have helped me by approving a southbound turn; but some of the Controllers at D-10 Approach have a less than a helpful attitude; yet they ask the Tower Controllers for help all the time with spacing and sequencing and things of that nature. I thought I had a way out by stopping the second aircraft at 3;000 FT; but the B727 was just too slow and low; and the HS25 was just too fast. I had no way of knowing that until he tagged up off the departure end of the runway.