# This Walled Pressure Vessels – Hot Dogs!

### Model Description

This is a simple demonstration of the basic principals underlying the behavior of thin-walled pressure vessels (TWPVs).  A hot dog is used to show that hoop stresses are twice as high as longitudinal stresses in cylindrical pressure vessels and failure occurs along the length of the hot dog.  The failure that occurs in the hot dog is due to hoop stress.  This demonstration should take 8-10 minutes.

### Engineering Principle

The basic derivation for TWPV behavior states that for a cylindrical pressure vessel:

$\sigma_{hoop} = \frac{P\cdot r}{t}$

$\sigma_{longitudinal} = \frac{P\cdot r}{2t}$

where the hoop stress is equal to the pressure times the inner radius divided by the wall thickness.  The longitudinal stress is exactly half the hoop value.  Therefore, a thin-walled pressure vessel is expected to fail due to hoop stress long before failure due to longitudinal stress.

### What You Need

Item Quantity Description/Clarification
Hot Dog varies At a minimum, use one regular hot dog per class.  To enhance the demo provide one hot dog per student.  Put a small slit in the hot dog (if necessary) to get it to fail from hoop stress.
Microwave 1
Refrigerator 1 Ensure your materials remain fresh!
Hot Dog Rolls, Condiments, Aluminum Foil Lots These items are optional, but will enhance the presentation of the training aids.

### How It’s Done

Before Class: Heat the hot dog in the microwave until it’s fully cooked (figure below, top). Check to ensure the hot dog clearly failed down the longitudinal axis due to hoop stress (figure below, bottom). You may have a defective hot dog which fails due to an improper seal at one end, so be prepared to cook more than one.

In Class:

Ask the class for different examples of thin walled pressure vessels.  Steer the students into giving examples of foods which behave as TWPV’s.  After hearing a few examples, try to get the student to say, “hot dog”.  At this point, pull the hot dog out and show the students.

Observations: The students should observe that the hot dog, cylindrical in shape, failed down it’s length.  This demonstrates that when the magnitude of the internal pressure increased, the hoop stress increased at twice the rate of longitudinal stress.  Therefore, in a cylindrical TWPV, hoop stress will cause failure before longitudinal stress.

Additional Application: Don’t merely take the hot dog out to show the students!  When it’s time to display the hot dog, the professor usually complains that he/she is really hungry.  To make matters worse, there was someone working in the classroom earlier and threw out some food in the trash can.  At this point the professor grabs the trash can to see if there’s any leftover food.  To his/her surprise there is a half eaten hot dog with mustard and ketchup in the trash. At this point the professor says, “Wait a minute, this hot dog reminds me of a thin walled pressure vessel!  Let’s see what happened when it was heated up!”  At this point the hot dog is revealed to the students and the hoop stress discussion begins.  Usually the students suggest eating the hot dog out of the trash.  Although optional, eating the hot dog really gets the attention of the students!  Afterwards, hand out one pre-heated hot dog to each student to observe the hoop stress failure.

### Cite this work as:

Matt Morris and Led Klosky (2019), "This Walled Pressure Vessels - Hot Dogs!," https://www.handsonmechanics.org/mechanics-of-materials/711.