The stress that unzips a pipe
Put pressure inside a thin-walled cylinder and the wall is pulled two ways at once. The bigger of the two runs around the girth, and it is called the hoop or circumferential stress: . Read aloud: sigma-h equals p d over two t. is the hoop stress in MPa; is the internal gauge pressure in MPa — gauge, so atmospheric pressure outside is already netted off; is the internal diameter in mm; and is the wall thickness in mm. Solve it for whichever one the question withholds.
You will meet the same relation written , with the internal RADIUS. Those are the same equation — the 2 in the denominator is exactly the conversion from diameter to radius. What is not the same is feeding a diameter into the pr/t form, which doubles your answer and is the classic wrong number on this topic. Pick one form and read the given carefully.
One quiet gift: with p in MPa and both lengths in mm, the millimetres cancel and the answer arrives in MPa with no conversion owed. That is not luck — a megapascal IS a newton per square millimetre. Thin-wall, incidentally, means above about 20; below that the stress varies through the wall and this formula starts telling comfortable lies.