Lectures 13-14

Question 1

Circumferential (hoop) stresses equation for the force equilibrium. Explain each variable.

Answer 1

2 (σ1 (t . dy)) - P (2r . dy) = 0

‘2’ - as the cross section of the thin walled vessel has the top and bottom thin wall
‘σ1’ - is the hoop stress
‘ (t . dy) ‘ - area of each small section of the thin walled vessel
‘P’ - vessel pressure

Question 2

Longitudinal stresses

Answer 2

σ2 (2 pi r t) - p (

Question 3

Why do we only consider the horizontal component of the pressure of the fluid applied on the inside of the vessel?

Answer 3

As all the vertical components cancel each other out, eg for the vertical forces, there is one applied upwards and one applied downwards.

The horizontal components of every force are remaining as the semi-circular portion of the tube is taken, thus the other side is not considered.

Question 4

Simplifying the equilibrium forces of hoop stresses, σ1 = ?

Answer 4

σ1 = p r / t

where P is the vessel pressure, r is the radius of the tube and t is the thickness of the vessel

Question 5

Longitudinal stress force equilibrium equation

Answer 5

σ2 (2π . r . t) - p (π r^2) = 0

where the longt. stress is acting in the opposite direction of the fluid pressure in the vessel

Question 6

Longitudinal stress equation simplified, σ2 = ?

Answer 6

σ2 = p r / 2 t

Question 7

In a cylindrical vessel, what relationship does the hoop stress have with longitudinal stress?

Answer 7

Hoop stress is twice as large as the longitudinal stress