Minor loss due to sudden expansion

[foo9008]

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 ?

 

[SteamKing]

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

 

[foo9008]

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 the energy loss between c and 2 is greater than the energy loss at (1 and c) ?

 

[SteamKing]

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 the 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.

 

[foo9008]

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

Can you explain further??

 

[SteamKing]

Can you explain further??

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

 

[foo9008]

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??

 

[SteamKing]

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.

 

[foo9008]

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.