The calculated distance (air line) between Wad az Zāki and Omdurman is approximately 84 miles respectively 135 kilometers.
By car or train, the actual journey to Omdurman is certainly longer, as only the direct route (as the crow flies) between Wad az Zāki and Omdurman has been calculated here.
Air line (approximately)
135 kilometers
73 nautical miles