Hydraulics
Prof. B.S. Thandaveswara
(i) Rotational and Irrotational flow
Flow
Radial motion or Radial flow
Rotary or Vortex Motion
Free vortex
Free Cylindrical Vortex
Forced vortex
Free Spiral vortex
Forced Cylindrical Vortex Forced Spiral vortex
Basically there are two types of motion
(i) Translation and
(ii) Rotation
The two may exist independently or simultaneously.
If now an element is represented, it may be subjected to deformation. This can be linear
or angular.
If the motion of the particles is purely translational and the distortion is symmetrical, the
flow is irrotational and the vorticity
⎛ ∂v y ∂vx
⎞
−
=cons tant ⎟⎟ .
⎜⎜
x
y
∂
∂
⎝
⎠
Example: Flownet application.
Forced vortex is also known as flywheel vortex.
Free vortex is also known as potential vortex.
v
=C
r
vr =C
Compound vortex combination of free and forced vortex also known as Rankine vortex.
Spiral vortex (free vortex and a radial flow).
Rotation of a fluid, moving as a solid, about an axis is called forced vortex motion. Every
particle of fluid will have same angular velocity.
Free vortex motion:
Each particle moves in a circular path with speed varying inversely as the distance from
the centre
vr =cons tant
Indian Institute of Technology Madras
.
Hydraulics
Prof. B.S. Thandaveswara
ω
r0
ω2r2
______
Paraboloid
2g
C
L
Forced vortex
v
=cons tant
r
. Rotation of the fluid in a tea cup is an example of a forced vortex.
ω
Sharp curved orifice
Bath tub vortex
(Basic vortex)
Vortex
Rotational flow
Irrotational flow
Application
(i) Vertical intake in Reservoir
(ii) Horizontal intake
(iii) Pump sump intake
Indian Institute of Technology Madras
Hydraulics
Prof. B.S. Thandaveswara
1
surface vortex
2
subsurface vortex
(submerged or underwater vortex)
1
(a)
2
(b)
(c)
1
local vortex
2
concentric or column vortex
Open air-core
(vortex orifice flow)
dimple
line vortices
Types of vortices due to location of appearance and resulting shape
1
2
3
description
due to:
1) increase of circulation
2) development relative to
the intake
3) Physical
explanation
weak
undeveloped
combined potential
and rotational vortex
(Rankine vortex)
critical
critical
critical stage
for air-entrainment
strong
developed
potential vortex or free
spiral vortex with an
open air-core
The different types of stable surface vortices at intakes vertically
downstream (drain vortices), indication and distinction
Indian Institute of Technology Madras
Hydraulics
Prof. B.S. Thandaveswara
r
Vt Tangential velocity
Free Vortex
Γ
Vt = ____
2-r r
Forced vortex
Vt = ωr
ξ
(vorticity)
2ω
Combined vortex
Indian Institute of Technology Madras
Hydraulics
Prof. B.S. Thandaveswara
o
rc
Flow around a 90 bend ___ = 0.5
b
Zone of seperation, Shock waves and Hydraulic jump can be seen
in the downstream of the bend (after Thandaveswara)
(iv) Cyclone.
Rankine vortex is a combination of free and forced vortex.
Forced vortex (inner core region) and Free vortex (in outer core region).
Free vortex tangential velocity
Pressure distribution
Velocity distribution
2ro
Rankine vortex
v = wr
t
C
v =
,r <r
t 2π r o
Vortices can be classified based on vortex strength. A basic vortex also referred as bath
tub vortex.
Indian Institute of Technology Madras