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Does the blood pressure at the root of aorta equal the blood pressure in the brachial artery?
I've heard it does, but it doesn't quite seem to make sense as I'd think the blood pressure would be lowered the further it travels?
Blood pressure is mostly dependent on the height from the heart. Therefore, if it is below the heart it will have higher blood pressure and if it is above the heart it will have lower blood pressure.
Here you are asking from two parts of body that have same height as the heart,
so they will have approximately the same blood pressure.
For more see: Netter's Anatomy Page 136 and Campbell Biology