Flow in pipes with sudden contraction

Underlying Flow Regime 4-14 © copyright ERCOFTAC 2004

References

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Nomenclature

d	Small tube diameter	Re	Reynolds Number
D	Large tube diameter	Red	Small tube outlet Re
K	Kinetic turbulent energy	ReD	Large tube inlet Re
K_L	Pressure loss coefficient	u	Axial fluid velocity
l	Small tube length	U1	Inlet average velocity
L	Large tube length	U2	Outlet average velocity
Ls1x	Upstream separation length	ucl	Centre-line fluid velocity
Ls1r	Upstream separation height	v	Radial fluid velocity
Ls2x	Downstream separation length	x	Axial distance from contraction plane
Ls2r	Downstream separation height	y	Radial distance
Lx,th	Throat axial location of downstream sep.	b	Contraction ratio (d/D)
p	Static Pressure	m	Fluid dynamic viscosity
ptot	Total Pressure	r	Fluid density
R	Pipe radius	s	Contraction area ratio

APPENDIX A

Pressure Loss Coefficient

The pressure loss coefficient for a sudden contraction is defined as

where Dp_t12is the total pressure loss due to the contraction, and ½ r U₂²is the kinetic pressure at Station 2 (see Fig.1). Dp_t12is defined as the total pressure drop between Station 1 in the large pipe and Station 2 in the small pipe minus the losses due to friction for fully developed flow in the large and small pipes extrapolated to the contraction plane. Station 1 and 2 are located in the fully developed regions upstream and downstream of the contraction respectively, outside the region of influence of the contraction. The total pressure loss Dp_t12is derived from measurements of static pressure loss Dp₁₂.