Page 95 - Fluid Power Engineering

70 Cha pte r T h ree

FIGURE 3.7 Sudden expansion.

FIGURE 3.8
Sudden contraction.

The local loss coefficient for sudden contraction is

⎛ D 2 ⎞ ρ v 2
ξ= 05 1 − 2 2 ⎟ ⎠ and ΔP =ξ 2 (3.6)
.
⎜
⎝
D 1 2
The values of the local loss coefficient ξ for a sudden contraction
element are given in Table 3.4.

3.4.2 Friction Losses
The pressure losses in the pipe lines depend mainly on the geometry,
surface roughness, fluid properties, and Reynolds number.
The three main types of flow are laminar, turbulent, and transi-
tion flow. Laminar flow is a streamlined flow of viscous fluid, where
all particles of the fluid move in distinct and separate lines. For New-
tonian fluids, the velocity distribution across the cross section of the
pipe is parabolic, with zero velocity in the vicinity of the pipe wall
and maximum velocity at the pipe center (see App. 2B). Figure 3.9
shows the development of laminar flow in a pipe. The transition
length, where the full laminar flow profile is not yet established,

D /D 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2 1
w 0.48 0.455 0.42 0.375 0.32 0.255 0.18

TABLE 3.4 Local Loss Coefficient for Sudden Contraction