Agarwal was the Chair of the Aerospace Engineering Department at Wichita State University from 1994 to 1996 and the Executive Director of National Institute for Aviation Research from 1996 to 2001. From 1994 to 2001, he was also the Bloomfield Distinguished Professor at Wichita State University.
Agarwal worked in various scientific and managerial positions at McDonnell Douglas Research Laboratories in St. Louis. He became the Program Director and McDonnell Douglas Fellow in 1990. From 1976 to 1978, Agarwal worked as a NRC Research Associate at NASA Ames Research Center and as a Principal Research Engineer at Rao and Associates in Palo Alto, California from 1975 to 1976.