Fluid Flow Characteristics

Flow   characteristics    deals    with   the   methods    of    determining   velocity   and acceleration. The fluid flow is classified as given below:

a) Steady and Unsteady Flows:

•    Steady flow is defined as  that  type  of  flow in  which the  fluid characteristics like velocity, pressure, density, etc. at a point do not change with time.

•    Unsteady flow is that type of flow, in which the velocity, pressure of density
at a point changes with respect to time.

b) Uniform and Non-uniform Flows:

•    Uniform flow is defined as that type of flow in which the velocity at any given time  does not change  with  respect  to space  (i.e., length  of  direction  of  the flow).

•    Non-uniform flow is that type of flow in  which the velocity at any given time changes with respect to space.

c) Laminar and Turbulent Flows:

•    Laminar flow is defined as that type of flow in which the fluid particles move along well-defined paths or stream lines and all the stream-lines are straight and parallel. Thus the particles move in laminas or layers gliding smoothly over the adjacent layer.  This type of flow is also called stream-line flow or viscous flow.

•    Turbulent flow is that type of flow in which the fluid particles move in zig-zag way. Due to the movement of fluid particles in a zig-zag way, the eddies formation takes place which the responsible for high energy loss. For a pipe flow, the type of flow is determined by a non-dimensional number VD/v called the Reynolds number, where D = Diameter of pipe; V = Mean velocity of flow in pipe; and v = Kinematic viscosity of fluid.

•    If the  Reynolds  number  is less  than  2000,  the flow is called  laminar.  If  the Reynolds  number  is  more  than  4000,  it  is  called  turbulent  flow.  If  the Reynolds  number  lies  between  2000  an  4000,  the  flow may  be laminar  or turbulent.

d) Compressible and Incompressible Flows:

•    Compressible flow is that type of flow in which the density of the fluid change from point to  point or in  other  words  the  density  (ȡ) is  not constant for  the fluid flow.

•    Incompressible flow is that type of flow in which the density of the fluid does not change from point to point or in other words  the density (ȡ) is constant for the fluid flow.

e) Rotational and Irrotational Flows:

•    Rotational  flow is that  type  of flow in  which  the fluid  particles  while flowing along stream-lines also rotate about their own axis.

•    If the fluid particles while flowing along stream-lines, do not rotate about their own axis, that type of flow is called irrotational flow.

f) One, Two and Three Dimensional Flows:

One-dimensional flow is that type of flow in which the flow parameter such as
velocity is  a  function  of  time  and  one  space  co-ordinate only, say x. For a steady one dimensional flow, the velocity is a function of one-space-co-ordinate only. The variation  of  velocities  in  other  two  mutually  perpendicular  directions  is  assumed negligible.

Two-dimensional flow is that type of flow in which the velocity is a function of
time  and  two  rectangular  space  co-ordinates  say  x  and  y.  For  a  steady  two- dimensional  flow  the  velocity  is  a  function  of  two  space  co-ordinates  only.  The variation of velocity in the third direction is negligible.

Three-dimensional flow is that type of flow in which the velocity is a function of
time and three mutually perpendicular directions. But for a steady three-dimensional flow the fluid parameters are functions of three space co-ordinates (x y and z) only.

Rate of Flow or Discharge (Q):
It is defined as the quantity of a fluid flowing per second through a section of a pipe
or a channel. For an incompressible fluid (or liquid) the rate of flow or discharge is expressed  as  the  volume  of  fluid  flowing  across  the  section  per  second.  For compressible  fluids,  the  rate  of  flow  is  usually  expressed  as  the  weight  of  fluid following across the section. Thus For liquids the units of Q are m3/sec of litres/sec
For gases and units of Q is kgf/sec or Newton/sec Consider a liquid flowing through
a pipe in which A=Cross-sectional area of pipe. V=Average velocity of fluid across the section.
Then discharge Q = A x V

Continuity Equation:

Let us make the mass balance for a fluid element as shown below-an open-faced cube):

Mass balance:

Accumulation  rate  of  mass  in  the  system  =  all  mass  flow rates  in  -  all  mass  flow rates out    --------------------- (1)
The  mass  in  the  system  at  any  instant  is  ȡ    x    y    z.  The  flow  into  the  system
through face 1 is
m1  =   ȡ1 vx1     y   z.
And the flow out of the system through face 2 is m2  =   ȡ2 vx2     y   z.
Similarly for the faces 3, 4, 5, and 6 are written as follows:

m3  =    ȡ3 vx3    x    z.
m4  =    ȡ4 vx4    x    z.

Substituting these quantities in equn.1, we get

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