What is the Formula for Minor Loss Due to Expansion?

In summary, the formula for minor loss due to contraction can be expressed as k[(mean velocity)^2]/2g, while the formula for minor loss due to expansion is also k[(mean velocity)^2]/2g, with the mean velocity being the velocity averaged over the cross section of the pipe. The old thread (post #1) considers a special case where V = 0. In the current thread, there is no contraction at CD and V1 plays the role of Vc, while V1 and V2 are linked through continuity. Therefore, you can get a kL for V2, but also a different kL for V1. The mean velocity is not suitable and should be replaced by V1 (mean velocity
  • #1
foo9008
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4

Homework Statement


from the previous thread , https://www.physicsforums.com/threads/minor-loss-in-pipe.869148/
, i know that formula of loss due to contraction can also be expressed as k[( mean velocity )^ 2 ] / 2g
how about the formula of minor loss due to expansion , can we expressed as k[( mean velocity )^ 2 ] / 2g ??

Homework Equations

The Attempt at a Solution

 

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  • #2
is it feasible ?
 
  • #3
What mean velocity did you have in mind ? ##V_1+ V_2\over 2\ \ ## ?

Or ##k_1 ## in combination with ##V_1## ?

The old thread is a 'special case' with one of the V = 0
 
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  • #4
BvU said:
What mean velocity did you have in mind ? ##V_1+ V_2\over 2\ \ ## ?

Or ##k_1 ## in combination with ##V_1## ?

The old thread is a 'special case' with one of the V = 0

Really, the old thread has one of the v =0 ? At which region?
For the loss due to expansion, I mean (V1 +V2 ) /2
 
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  • #5
in the old thread , how can one of the v = 0 ? it is [(Vc -V2)^2]/ 2g
 
  • #6
foo9008 said:
Really, the old thread has one of the v =0 ? At which region?
For the loss due to expansion, I mean (V1 +V2 ) /2
What do you mean by combination of k and v1 ?
 
  • #7
foo9008 said:
At which region?
in the reservoir
foo9008 said:
For the loss due to expansion, I mean (V1 +V2 ) /2
well, the link gives the expressions. You can try to wiggle ##\ \
\left (V_1+ V_2\over 2\right )^2 \ \ ## into this but i doubt that succeeds...
 
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  • #8
foo9008 said:
in the old thread , how can one of the v = 0 ? it is [(Vc -V2)^2]/ 2g
I meant the one in post #1
 
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  • #9
BvU said:
in the reservoir
well, the link gives the expressions. You can try to wiggle ##\ \
\left (V_1+ V_2\over 2\right )^2 \ \ ## into this but i doubt that succeeds...
So , its not possible to change the to change the original formula of head loss due to expansion into
k[( mean velocity )^ 2 ] / 2g??
 
  • #10
BvU said:
it doesn't state v = 0 , it just stated mean velocity in 165
 
  • #11
Ah ! I was mistaken in post #3. In 165 there is no counterpart of the ##V_1## in 166 -- so I wanted to consider ##V_1## as zero in picture 165. But it plays no role in either case: the ##v## involved are ## V_c## and ##V_2## in both cases, so 165 and 166 say the same (as haru indicated and you Ok'd)

(we are now talking about pictures in another thread - never mind :smile:) .

In 166 you see a ## k_L = \left ( {\displaystyle A_2\over \displaystyle A_c} - 1\right )^2##.

In the current thread the idea is that there is no contraction at CD and that means ##V_1## plays the role of ##V_c## (and ##A_1## is ##A_c##).

##v_1## and ##v_2## are linked through continuity (##V_1 A_1 = V_2 A_2##) so -- analogous to 166 -- you get a ##k_L## for ##V_2## but you can also get a (different) ##k_L## for ##V_1##.

'Mean velocity in the pipe' may have caused confusion: what is meant is volume flow divided by area (i.e. the velocity averaged over the cross section -- so not lengthwise). In other words: there is no place for (V1 +V2 ) /2
 
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  • #12
BvU said:
Ah ! I was mistaken in post #3. In 165 there is no counterpart of the ##V_1## in 166 -- so I wanted to consider ##V_1## as zero in picture 165. But it plays no role in either case: the ##v## involved are ## V_c## and ##V_2## in both cases, so 165 and 166 say the same (as haru indicated and you Ok'd)

(we are now talking about pictures in another thread - never mind :smile:) .

In 166 you see a ## k_L = \left ( {\displaystyle A_2\over \displaystyle A_c} - 1\right )^2##.

In the current thread the idea is that there is no contraction at CD and that means ##V_1## plays the role of ##V_c## (and ##A_1## is ##A_c##).

##v_1## and ##v_2## are linked through continuity (##V_1 A_1 = V_2 A_2##) so -- analogous to 166 -- you get a ##k_L## for ##V_2## but you can also get a (different) ##k_L## for ##V_1##.

'Mean velocity in the pipe' may have caused confusion: what is meant is volume flow divided by area (i.e. the velocity averaged over the cross section -- so not lengthwise). In other words: there is no place for (V1 +V2 ) /2

ok , i understand that the velocity is average velocity across the area , but can still i say that the head loss due to contraction expansion is k[( mean velocity^2] / 2g ?
 
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  • #13
BvU said:
Ah ! I was mistaken in post #3. In 165 there is no counterpart of the ##V_1## in 166 -- so I wanted to consider ##V_1## as zero in picture 165. But it plays no role in either case: the ##v## involved are ## V_c## and ##V_2## in both cases, so 165 and 166 say the same (as haru indicated and you Ok'd)

(we are now talking about pictures in another thread - never mind :smile:) .

In 166 you see a ## k_L = \left ( {\displaystyle A_2\over \displaystyle A_c} - 1\right )^2##.

In the current thread the idea is that there is no contraction at CD and that means ##V_1## plays the role of ##V_c## (and ##A_1## is ##A_c##).

##v_1## and ##v_2## are linked through continuity (##V_1 A_1 = V_2 A_2##) so -- analogous to 166 -- you get a ##k_L## for ##V_2## but you can also get a (different) ##k_L## for ##V_1##.

'Mean velocity in the pipe' may have caused confusion: what is meant is volume flow divided by area (i.e. the velocity averaged over the cross section -- so not lengthwise). In other words: there is no place for (V1 +V2 ) /2
sorry , pls ignore my several posts before this . do you mean the mean velocity is not suitable and should be replaced by v1(mean velocity at region 1 ) or v2( mean velocity at region 2 ) to avoid confusion ?
 
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What is minor loss due to expansion?

Minor loss due to expansion is the reduction in fluid pressure that occurs when a fluid flows through a pipe or channel with an increasing cross-sectional area.

What causes minor loss due to expansion?

Minor loss due to expansion is caused by the conversion of kinetic energy into potential energy as the fluid expands into a larger area. This results in a decrease in fluid pressure.

How is minor loss due to expansion calculated?

Minor loss due to expansion is calculated using the Bernoulli's equation, which takes into account the fluid velocity, density, and the change in cross-sectional area.

What are some examples of minor loss due to expansion?

Some examples of minor loss due to expansion include the sudden expansion of a pipe, the entrance of a pipe into a larger tank, or the exit of a pipe from a smaller tank.

How can minor loss due to expansion be minimized?

To minimize minor loss due to expansion, it is important to design pipes and channels with gradual transitions in cross-sectional area, rather than sudden changes. Additionally, using smooth and streamlined fittings can also help reduce minor loss due to expansion.

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