×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs
Home > Forums > Mechanical Engineers > Activities > Pipelines, Piping and Fluid Mechanics engineering > FAQs

Pipelines, Piping and Fluid Mechanics engineering FAQ

Expansion and flexibility

Pressure increase due to thermal expansion of a trapped liquid by prex
faq378-1339
Posted: 25 May 07

The calculation of pressure increase due to thermal expansion of a liquid fully filling, without any gas bubbles or pockets, a metallic enclosure, may be treated as follows.
The phenomena to be considered are:
1)thermal expansion of liquid due to the change of its bulk temperature
2)thermal expansion of the vessel or pipe, assumed in the following as having the same temperature as the fluid
3)compressibility of liquid under the increase in pressure due to the constrained volume
4)increase in volume of the vessel under the increased pressure of the fluid.
The corresponding contributions to the relative change in volume δV/V of fluid or of the containing space may be evaluated as follows:
1)αfΔT
2)αvΔT
3)βΔP
4)ΔPD/tE
where:
-αf is the volumetric coefficient of thermal expansion of the fluid
-αv is the volumetric coefficient of thermal expansion of the vessel (= three times the linear one)
-ΔT is the change in temperature
-β is the compressibility factor of the fluid, or the relative change in volume per unit change in pressure
-ΔP is the change in pressure of the fluid (it is what we seek)
-D,t and E are respectively the diameter, the thickness and the elastic modulus of the vessel (or pipe)
By equating the change in volume of the fluid to the change in volume of the vessel one gets:
αfΔT-βΔP=αvΔT+ΔPD/tE
or
ΔP=(αf-αv)ΔT/(β+D/tE)

Let's take as an example water as the entrapped fluid and carbon steel for the container, at temperatures not far from room temperature.
We have:
αf=210x10-6 ¦C-1
αv=36x10-6 ¦C-1
β=4x10-4 MPa-1
E=2x105 MPa
D/t will of course widely vary according to the dimensions and design pressure of the container; we may assume a variation between 100 for a light vessel or pipe and 10 for a quite heavy vessel, the value of 0 corresponding to an infinitely rigid container.
With these figures we get (per degree C of change in temperature):
ΔP=0.19 MPa =~ 2 bar for the light container
ΔP=0.39 MPa =~ 4 bar for the heavy container
ΔP=0.44 MPa =~ 4.4 bar for the rigid container
 

Back to Pipelines, Piping and Fluid Mechanics engineering FAQ Index
Back to Pipelines, Piping and Fluid Mechanics engineering Forum

My Archive


Resources

White Paper - A Guide to 3D Printing Materials
When it comes to using an FDM 3D printer effectively and efficiently, choosing the right material at the right time is essential. This 3D Printing Materials Guide will help give you and your team a basic understanding of some FDM 3D printing polymers and composites, their strengths and weaknesses, and when to use them. Download Now
Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close