Minor Loss in Pipe: Which Formula?

[foo9008]

Homework Statement

which formula is correct ? the formula in the first ? or in the second ? one is using the mean velocity , while the another one is using velocity difference between vena contarcta and velocity at exit ...

Homework Equations

The Attempt at a Solution

 

[haruspex]

Homework Statement

which formula is correct ? the formula in the first ? or in the second ? one is using the mean velocity , while the another one is using velocity difference between vena contarcta and velocity at exit ...

Homework Equations

The Attempt at a Solution

No, both end up referencing the mean velocity in the continuing pipe. The k factor comes from how that velocity relates to the velocity difference from the fastest velocity.

 

[foo9008]

No, both end up referencing the mean velocity in the continuing pipe. The k factor comes from how that velocity relates to the velocity difference from the fastest velocity.

do you mean none of them are correct , then what is the correct formula , can you show it ?

 

[haruspex]

do you mean none of them are correct , then what is the correct formula , can you show it ?

No, I mean the two are saying the same.

 

[foo9008]

No, I mean the two are saying the same.

ok

 

[foo9008]

No, both end up referencing the mean velocity in the continuing pipe. The k factor comes from how that velocity relates to the velocity difference from the fastest velocity.

are you referring to 165?

 

[foo9008]

No, both end up referencing the mean velocity in the continuing pipe. The k factor comes from how that velocity relates to the velocity difference from the fastest velocity.

the velocity means the velocity throughout the pipe and reservoir ?

 

[haruspex]

the velocity means the velocity throughout the pipe and reservoir ?

Both are interested in the mean velocity further along the pipe. 165 calls this v₂; 166 calls it $\bar v$. The equation in 165 relates it to h_e and k_e; 166 has the same equation, at the end, but calls them h_L and k_L.
The remaining equations in 166 show how this equation is obtained. 165 omits that.

 

[foo9008]

Both are interested in the mean velocity further along the pipe. 165 calls this v₂; 166 calls it $\bar v$. The equation in 165 relates it to h_e and k_e; 166 has the same equation, at the end, but calls them h_L and k_L.
The remaining equations in 166 show how this equation is obtained. 165 omits that.

i assume you said that the v is for 165 , while v_2 is for 166 , can you explain what does the v mean ? v means mean velocity at which region ? the v_2 mean the velocity at area 2 , am i right ?

 

[haruspex]

i assume you said that the v is for 165 , while v_2 is for 166 , can you explain what does the v mean ? v means mean velocity at which region ? the v_2 mean the velocity at area 2 , am i right ?

Yes, sorry, I wrote those two backwards.
It describes v₂ as the mean velocity in the pipe. You can think of that either as the mean velocity across the whole width of the pipe where the vena contracta is, or as the actual velocity much further along the pipe. The two must be the same by conservation of volume flow rate.

 

[foo9008]

Yes, sorry, I wrote those two backwards.
It describes v₂ as the mean velocity in the pipe. You can think of that either as the mean velocity across the whole width of the pipe where the vena contracta is, or as the actual velocity much further along the pipe. The two must be the same by conservation of volume flow rate.

Do you mean v in the 165 is the mean velocity at the vena contrava ??

 

[foo9008]

Yes, sorry, I wrote those two backwards.
It describes v₂ as the mean velocity in the pipe. You can think of that either as the mean velocity across the whole width of the pipe where the vena contracta is, or as the actual velocity much further along the pipe. The two must be the same by conservation of volume flow rate.

Why we can consider it as velocity further from the pipe?

 

[foo9008]

Yes, sorry, I wrote those two backwards.
It describes v₂ as the mean velocity in the pipe. You can think of that either as the mean velocity across the whole width of the pipe where the vena contracta is, or as the actual velocity much further along the pipe. The two must be the same by conservation of volume flow rate.

Why we can consider it as velocity further from the pipe?

 

[haruspex]

Why we can consider it as velocity further from the pipe?

If you take a section right through the pipe at any point along it, the net volume flow rate through it must be the same at all points. If not, liquid is being created or destroyed somewhere. So the average velocity, taken across the whole width of the pipe, must also be constant along the pipe.
As one of the diagrams shows, at the vena contracta the velocity might be negative at the sides (a backwater), but so great in the centre that the average over the whole width is just the same as further along the pipe.

 

[foo9008]

If you take a section right through the pipe at any point along it, the net volume flow rate through it must be the same at all points. If not, liquid is being created or destroyed somewhere. So the average velocity, taken across the whole width of the pipe, must also be constant along the pipe.
As one of the diagrams shows, at the vena contracta the velocity might be negative at the sides (a backwater), but so great in the centre that the average over the whole width is just the same as further along the pipe.

I didn't see the velocity of water is negative, can you point out which part??

 

[haruspex]

I didn't see the velocity of water is negative, can you point out which part??

The diagram in 166 shows a reverse flow either side of the main flow at the vena contracta.

 

[foo9008]

The diagram in 166 shows a reverse flow either side of the main flow at the vena contracta.

You said that we can consider the velocity away from the pipe? You mean velocity after the vena contrava , am I right??

 

[haruspex]

You said that we can consider the velocity away from the pipe? You mean velocity after the vena contrava , am I right??

The mean velocity in the pipe is the same all the way along it. As I posted,that follows immediately from the fact that it is an incompressible liquid. If you want to suppose that eventually, well down the pipe, the velocity is the same across the whole width of the pipe then, yes, that will all be at that mean velocity.