Hydraulic and energy gradient - Laminar flow through circular conduits and circular annuli- Boundary layer concepts – types of boundary layer thickness – Darcy Weisbach equation –friction factor- Moody diagram- commercial pipes- minor losses – Flow through pipes in series and

1. UNIT - 2
FLOW THROUGH
CIRCULAR CONDUITS

3. STEADY FLOW: A flow in which the velocity, pressure, density, etc., Of the
fluid at a particular fixed point does not change with time —called also
stationary flow. An example is the flow of water in a pipe of constant
diameter at constant velocity.
UNSTEADY FLOW: A flow in which the velocity, pressure, density, etc., Of the
fluid at a particular fixed point change with time.

4. UNIFORM FLOW: The flow is defined as uniform flow when in the flow
field the velocity and other hydrodynamic parameters do not change from
point to point at any instant of time.
NON-UNIFORM FLOW: When the velocity and other hydrodynamic
parameters changes from one point to another the flow is defined as non-
uniform.

5. LAMINAR FLOW: The flow of a fluid when each particle of the fluid
follows a smooth path, paths which never interfere with one another. One
result of laminar flow is that the velocity of the fluid is constant at any
point in the fluid.
TURBULENT FLOW: Irregular flow that is characterized by tiny whirlpool
regions (or) in other words fluids particles move in a zig-zag way. The
velocity of this fluid is definitely not constant at every point.
 The type of flow is determined by a non-dimensional number VD/v is
called Renold number.
Renold number lessthan 2000, the flow is called laminar. If more than 4000,
it’s called turbulent flow. If Renold number lies b/w 2000 and 4000, the
flow may be laminar or turbulent.

6. COMPRESSIBLE FLOW: That type of flow in which the density of fluid
changes from point to point (or) in other words the density is not constant
for fluids.
INCOMPRESSIBLE FLOW: That type of flow in which the density is
constant for the fluid flow. Liquids are generally incompressible flow while
gases are compressible flow.

8. ONE-DIMENSIONAL FLOW: That type of flow in which the velocity is a
function of time and one rectangular space coordinate say x.
u=f(x), v=0 and w=o
TWO-DIMENSIONAL FLOW: That type of flow in which the velocity is a
function of time and two rectangular space coordinate say x and y.
u=f1(x,y), v=f2(x,y) and w=0
TWO-DIMENSIONAL FLOW: That type of flow in which the velocity is a
function of time and three mutually perpendicular directions. Three
coordinates are (x, y, z)
u=f1(x,y,z), v=f2(x,y,z) and w=f3(x,y,z)

9. BOUNDARY LAYER
• The fluid layer in the vicinity of the solid
boundary where the effect of fluid friction i.e.,
the variation of velocity are predominant is
known as boundary layer

14. Boundary layer thickness

15. Displacement thickness

17. Momentum thickness

18. Energy thickness

19. MOODY DIAGRAM

20. • Moody’s diagram is plotted between various
values of friction factor (f), Reynolds number
(Re) and relative roughness (R/K) .
• For any turbulant flow problem, the values of
fricton factors (f) can be determined from
Moody’s diagram, if the numerical values of
R/K for the pipe and Re of flow are known.

21. S.No Pipe Material K in mm
1 Glass, Brass, Copper Smooth
2 Lead 0.045
3 Steel, wrought Iron 0.12
4 Asphalted Cast iron 0.15
5 Galvanized iron 0.26
6 Cast iron 0.9 to 9.0