The scales of Raga Manirangu are as follows :
Aarohanam (Ascending) : S R2 M1 P N2 S’
Avarohanam (Descending) : S’ N2 P M1 G2 R2 S
It is a janya raga, derived from Kharaharapriya which is 22nd on the Melakarta scale. It is very close to Madhyamavati and Shreeraga. If you struggle with identifying the difference, here is a good demo here for Manirangu vs Shreeraga. It might also be worth listening to the difference between Madhyamavati vs Shreeraga. Well known kritis which come to mind are Mamava Pattabhirama by Muthuswami Dikshithar, Ranidhi Radu by Tyagaraja, Jaya Jaya Padmanabha by Swati Thirunal and Yaar Enna Sollalum by Oothukkadu Venkata Subbaiyer.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.