In order to make your Turkish coffee foamy (which is a must to achieve the proper taste) your coffee pot must be the right size. Thewater level in your pot needs to be some where close to the middle of your pot (or at least about 1/2 to1 inch below the rim). This off course will depend on how many cups of coffee you are makingand the size of your pot.
Please note that not all measuring cups are accurate. We use the newly updated glass Pyrex brand which is considered to be the most accurate measuring cup by professional cooks in US. It is made in USA. Here is a video by America's Test kitchen about measuring cups: