A dry powder inhaler for pulmonary or nasal use, comprising at least an inhaler body 801 and a cartridge 803 with at least one powder compartment 805 including one dose of a drug. The body has an opening 804 shaped for receiving the cartridge 803 and the means to allow a controlled sliding movement of the cartridge 803 relative to the body 801 after mounting. The cartridge powder compartment 805 comprises at least two inlets or slits 806, 809, at least one of which is a side inlet 809, for the admission of air, and a compartment outlet 807 to allow filling and fluid communication with an inhalation channel 808 provided in the body 801. In use, the patient slides the cartridge 803 relative to the body 801 from the storage position, where the inlets in the cartridge powder compartment 805 are blocked and sealed by walls comprised in the body 801, into the inhalation position, where the compartment inlets become available for the admission of air used in the dispersion of the particles there contained and the compartment outlet 807 becomes aligned with the inhalation channel 808 in the body 801 to allow the entrainment of the dose dispersed through the device and into the desired site of action during inhalation. The addition of one or more lateral vents 809 in the cartridge powder compartments induces a turbulent and swirling flow pattern that promotes improved dispersion and entrainment. The invention affords a very economical and simple device for the delivery of high dosages of inhaled medicines.