Minor loss due to sudden expansion

  • Thread starter foo9008
  • Start date
  • #1
678
4

Homework Statement


why the minor loss due to sudden expansion is given by formula of [( v_c - v_2) ^2 ]/ 2g ?

Homework Equations




The Attempt at a Solution


can it be [( v_2 - v_1) ^2 ]/ 2g ?
 

Attachments

  • Capture.PNG
    Capture.PNG
    25 KB · Views: 7,440

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670

Homework Statement


why the minor loss due to sudden expansion is given by formula of [( v_c - v_2) ^2 ]/ 2g ?

Homework Equations




The Attempt at a Solution


can it be [( v_2 - v_1) ^2 ]/ 2g ?
The graphic talks about head loss due to a sudden contraction.

The velocity vc is important because it represents the greatest velocity to which the fluid is accelerated as it passes thru the sudden contraction, and consequently, in the zone between station c and station 2 is where the greater amount of head loss occurs. Very little loss occurs in the zone between station 1 and station c.

For more information:

https://en.wikipedia.org/wiki/Borda–Carnot_equation
 
  • #3
678
4
The graphic talks about head loss due to a sudden contraction.

The velocity vc is important because it represents the greatest velocity to which the fluid is accelerated as it passes thru the sudden contraction, and consequently, in the zone between station c and station 2 is where the greater amount of head loss occurs. Very little loss occurs in the zone between station 1 and station c.

For more information:

https://en.wikipedia.org/wiki/Borda–Carnot_equation
from the link , i can undertstand the gretest amount of energy lost at region c , can the formula be [( v_c - v_1) ^2 ]/ 2g ? how do u know that teh energy loss between c and 2 is greater than the energy loss at (1 and c) ???
 
Last edited:
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670
from the link , i can undertstand the gretest amount of energy lost at region c , can the formula be [( v_c - v_1) ^2 ]/ 2g ? how do u know that teh energy loss between c and 2 is greater than the energy loss at (1 and c) ???
From the velocities. V1 < Vc and Vc > V2, based on the continuity equation. Plus, that's what the wiki article says. :smile::wink:
 
  • #5
678
4
From the velocities. V1 < Vc and Vc > V2, based on the continuity equation. Plus, that's what the wiki article says. :smile::wink:
Can you explain further??
 
  • #6
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670
Can you explain further??
What's not clear about "That's what the wiki article says"?
 
  • #7
678
4
What's not clear about "That's what the wiki article says"
It didn't explain why the calculation can't involve vc and v1??
 
  • #8
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670
Sure it did. You just don't want to accept it, for some reason.

To recap:
"There is not much head loss between cross section 1, before the contraction, and cross section 3, the vena contracta at which the main flow is contracted most. But there are substantial losses in the flow expansion from cross section 3 to 2."

In other words, the loss between v1 and vc is negligible compared to the loss between vc and v2. Since head loss is proportional to velocity squared, the loss caused by the difference in vc and v2 must be based on those two velocities, not on v1 and vc.
 
  • #9
678
4
noted
Sure it did. You just don't want to accept it, for some reason.

To recap:
"There is not much head loss between cross section 1, before the contraction, and cross section 3, the vena contracta at which the main flow is contracted most. But there are substantial losses in the flow expansion from cross section 3 to 2."

In other words, the loss between v1 and vc is negligible compared to the loss between vc and v2. Since head loss is proportional to velocity squared, the loss caused by the difference in vc and v2 must be based on those two velocities, not on v1 and vc.
 

Related Threads on Minor loss due to sudden expansion

  • Last Post
Replies
12
Views
983
Replies
3
Views
1K
Replies
2
Views
1K
Replies
2
Views
769
  • Last Post
Replies
3
Views
665
  • Last Post
Replies
17
Views
956
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
7
Views
907
  • Last Post
Replies
0
Views
5K
  • Last Post
Replies
3
Views
19K
Top