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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