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.