# Minor loss due to sudden expansion

1. Apr 24, 2016

### foo9008

1. The problem statement, all variables and given/known data
why the minor loss due to sudden expansion is given by formula of [( v_c - v_2) ^2 ]/ 2g ?

2. Relevant equations

3. The attempt at a solution
can it be [( v_2 - v_1) ^2 ]/ 2g ?

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2. Apr 24, 2016

### SteamKing

Staff Emeritus

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.

https://en.wikipedia.org/wiki/Borda–Carnot_equation

3. Apr 25, 2016

### foo9008

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: Apr 25, 2016
4. Apr 25, 2016

### SteamKing

Staff Emeritus
From the velocities. V1 < Vc and Vc > V2, based on the continuity equation. Plus, that's what the wiki article says.

5. Apr 25, 2016

### foo9008

Can you explain further??

6. Apr 25, 2016

### SteamKing

Staff Emeritus
What's not clear about "That's what the wiki article says"?

7. Apr 25, 2016

### foo9008

8. Apr 25, 2016

### SteamKing

Staff Emeritus
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. Apr 25, 2016

noted