Abstract
The laminar flow phenomena in the inlet (entrance) region of circular pipe are investigated experimentally. New curves of friction factor versus Reynolds number, for various entry lengths, are obtained and compared with the standard curve for fully developed laminar flow. The relationship between the viscous friction, the energy loss due to the lengthwise rate of change of the kinetic energy coefficient and the total energy loss is investigated. The continuous variation of the velocity profile is analysed by using the concept of a non-Newtonian liquid whose shear sensitivity varies continuously along the pipe.
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Abbreviations
- A :
-
cross-sectional area
- α :
-
kinetic energy correction coefficient
- D :
-
pipe diameter
- δ :
-
boundary thickness
- Δ:
-
increment
- f :
-
measured friction factor as defined by Darcy's law
- f k :
-
component of f due to change in kinetic energy only
- f v :
-
component of f due to viscous head loss only
- f L :
-
friction factor as computed from Langhaar's theory
- g :
-
gravitational acceleration
- h :
-
head loss
- H k :
-
component of h due to change in kinetic energy
- H v :
-
component of h due to viscous friction
- K, n :
-
constants in the power law τ=K(dU/dr)n
- v :
-
kinematic viscosity
- μ :
-
viscosity
- L :
-
length
- L e :
-
entry length
- L d :
-
developing (inlet) length
- N R :
-
Reynolds number
- P :
-
pressure
- Q :
-
volume discharge
- r :
-
distance from the centre line of the pipe towards the wall
- r 0 :
-
radius
- ρ :
-
pressure
- τ :
-
shear stress
- U :
-
velocity
- U m :
-
mean velocity
- U c :
-
centre-line (maximum) velocity
- x 1 :
-
axial distance from entrance to the first pressure tapping point
- x 2 :
-
axial distance from entrance to the second pressure tapping point
- Z :
-
dimensionless number=L/r 0
- ξ :
-
dimensionless number=Z/N R
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Al-Nassri, S.A., Unny, T. Developing laminar flow in the inlet length of a smooth pipe. Applied Scientific Research 36, 313–332 (1981). https://doi.org/10.1007/BF00411891
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DOI: https://doi.org/10.1007/BF00411891