Is D2/D1 = 0 the Ideal Condition for Pressure Loss in a Pipe?

[foo9008]

Homework Statement

what does the author mean by D2/ D1 = 0 ? when D2/ D1 = 0 , the pipe doesn't exist , right ?

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

what does the author mean by D2/ D1 = 0 ? when D2/ D1 = 0 , the pipe doesn't exist , right ?

Homework Equations

The Attempt at a Solution

Right. The limiting case when D2/D1 = 0 applies when fluid is flowing from a wide-open volume, say a reservoir, into a pipe suddenly. The diameter of flow from the reservoir D1 is so huge in comparison to the diameter of the pipe D2 that the quantity D2/D1 → 0 in the limit.

 

[foo9008]

Right. The limiting case when D2/D1 = 0 applies when fluid is flowing from a wide-open volume, say a reservoir, into a pipe suddenly. The diameter of flow from the reservoir D1 is so huge in comparison to the diameter of the pipe D2 that the quantity D2/D1 → 0 in the limit.

so it's not exactly = 0 , it's approaching 0 , am i right ?

 

[gmax137]

so it's not exactly = 0 , it's approaching 0 , am i right ?

Right. Think about a drain pipe going straight down from the floor of a swimming pool. The area of the pipe is negligible in comparison to the area of the pool. The next entry in the table is D2/D1 = 0.1, so the big pipe is ten times the diameter of the small pipe (and you use K=0.45). Anything much bigger than that, use 0.5.

Keep in mind these K factors are approximate; they will give you "pretty close" results. For really critical applications, pressure losses are determined by testing. If you're designing something where K=0.45 gives acceptable results but 0.5 does not, you need to re-think your approach.