Laminar Flow
Its is a flow in which the fluid particles move in parallel layers in a single direction.Due to the parabolic velocity distribution in laminar flow, a shearing stress is developed. As this shearing stress increases, the viscous forces become unable to damp out disturbances, and turbulent flow results. The region of change is dependent on the fluid velocity, density, and viscosity and the size of the conduit.
Reynolds number which is the ratio of inertial forces/viscous forces is basically used to determine the kind of flow that is whether it is laminar, turbulent or is in transition .
Reynolds number <2000 ==laminar
Reynolds number >2000 == turbulent.
R=VD$/u=VD/v
where
V=fluid velocity,ft/s(m/s)
D=pipe Diameter,ft(m)
$=density of fluid,lb-s2/ft4
u=viscosity of fluid lb-s/ft2(kg-s/m2)
v=u/$=kinematic viscosity,ft2/s(m2/s)
Diagram showing Laminar Flow
In laminar flow.the following equation for head loss due to friction can be developed by considering the forces acting on a cylinder of fluid in a pipe:
hf=32uLV/D2?g
where
hf=head loss due to friction,ft(m)
L=length of pipe section considered,ft(m)
g=Acceleration due to gravity(9.81 m/s2)
Turbulent Flow
The inertial forces are large due to which the viscous forces cannot dampen out the disturbances which in turn create eddies.These eddies have a rotational and translational velocity.
Factors Regarding Head Loss:
1) The head loss varies directly as the length of the pipe.
2) The head loss varies almost as the square of the velocity.
3) The head loss varies almost inversely as the diameter.
The head loss depends on the surface roughness of the pipe wall.
4) The head loss depends on the fluid density and viscosity.
5) The head loss is independent of the pressure.
Tuesday, May 5, 2009
Fluid Flow in Pipes
Stadia Surveying
In stadia surveying, a transit having horizontal stadia crosshairs above and below the central horizontal crosshair is used. The difference in the rod readings at the stadia cross hairs is termed the rod intercept. The intercept may be converted to the horizontal and vertical distances between the instrument and the rod by the following formulas:
H= Ki(cos a)2 ( f+c) cos a
V=0.5Ki(sin 2a)+( f +c) sin a
where
H= horizontal distance between center of transit and rod, ft (m)
V =vertical distance between center of transit and point on rod intersected by middle horizontal crosshair, ft (m)
K =stadia factor (usually 100)
i =rod intercept, ft (m)
a =vertical inclination of line of sight, measured from the horizontal, degree
f+c =instrument constant, ft (m) (usually taken as 1 ft) (0.3048 m)
For horizontal sights,the stadia distance ft(m) can be calculated as:
D=Rf/i+C
where
R= intercept on rod between two sighting wires, ft (m)
f =focal length of telescope, ft (m) (constant for specific instrument)
i distance between stadia wires, ft (m)
C= f+c
c= distance from center of spindle to center of objective lens, ft (m)
C is called the stadia constant, although c and C vary slightly. The value of f/i, the stadia factor, is set by the manufacturer to be about 100, but it is not necessarily 100.00. The value should be checked before use on important work,
or when the wires or reticle are damaged and replaced.
