1. Subject Name: FLUID MECHANICS
Subject Code:10ME36B
Prepared By: PUNITH R
Department: AE
Date:

2. Laminar Flows: Turbulent Flows:
Movement of any fluid particle is regular
Path lines of fluid particles are smooth
Turbulent Flows:
Movement of any fluid particle is random
Path lines of fluid particles are affected by mixing

3. Pipe flow head loss is proportional to the length of the pipe
proportional to the square of the velocity (high Reynolds number)
Proportional inversely with the diameter of the pipe
increasing with surface roughness
independent of pressure

4. Reynolds number
After exhaustive experiments in the 1880s, Osborne Reynolds discovered that the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid. This ratio is called the Reynolds number and is expressed for internal flow in a circular pipe as

5. Average velocity in a pipe because of the no-slip condition, the velocity at the walls of a pipe or duct flow is zero We are often interested only in V avg, which we usually call just V (drop the bitfi) subscript for convenience) Keep in mind that the no-slip condition causes shear stress and friction along the pipe walls

7. Loss of energy in pipes Classification 1. Major losses 2.Minor losses
It is due to friction
2.Minor losses
Sudden expansion of pipe
Sudden contraction of pipe
Bend in pipe
Pipe fittings
An obstruction in pipe

8. Major Losses The head loss, hL-major is given as ;
where f is friction factor.
Above mention equation is called the Darcy-Weisbach equation. It is valid for any fully developed, steady, incompressible pipe flow, whether the pipe is horizontal or on hill

9. Darcy-Weisbach Equation For loss of head due to friction in pipes
hf = (4fLV2 )/(d×2g)
Where,
hf = Head loss due to friction
V= mean Velocity of flow
L= length of pipe between two sections
f= Co-efficient of friction
d= diameter of the pipe
g= acceleration due to gravity
(f’/ρg)= f/2
f’= frictional resistance per unit wetted area per unit velocity

10. Chezy’s Equation For loss of head due to friction in pipes
C = sqrt(mi)
Where,
(ρg /f’)= C
f’= frictional resistance per unit wetted area per unit velocity
g= acceleration due to gravity
C= chezy’s constant
Value of m=Area/Perimeter= d/4 for pipe
hf /L =i
hf = Head loss due to friction
L= length of pipe between two sections
i= Loss of head per unit length of pipe

11. Minor losses Loss of head due to sudden expansion of pipe
Loss of head due to sudden contraction of pipe
Loss of head due to bend in pipe
Loss of head due to pipe fittings
Loss of head due to obstruction in pipe

12. Loss of head at entrance of pipe
hi =0.5(V2/2g)
Where,
V= Velocity of liquid in pipe
hi = Loss at exit of pipe

13. Loss of head at exit of pipe
ho = (V2/2g)
Where
V= Velocity of liquid in pipe
ho = Loss at entrance of pipe

14. Loss of head due to sudden expansion of pipe
he = (V1-V2)2/2g
Where
V1,V2= Velocity of liquid at area 1 and 2 in pipe
he = Loss at entrance of pipe

15. Loss of head due to sudden Contraction of pipe
hc = 0.5(V2)2/2g
Where
V2= Velocity of liquid at area 2 in pipe
hc = Loss at entrance of pipe

16. Total energy gradient line
It is equal to sum of pressure head ,velocity head and datum head
EL = H = p / W + v2 / 2 g + Z = constant along a streamline        
where
(EL ) Energy Line
For a fluid flow without any losses due to friction (major losses) or components (minor losses) - the energy line would be at a constant level. In a practical world the energy line decreases along the flow due to losses.
A turbine in the flow reduces the energy line and a pump or fan in the line increases the energy line

17. Hydraulic Grade Line (HGL )
Hydraulic gradient line is the sum of pressure head and datum head
HGL = p / W + Z       
where
The hydraulic grade line lies one velocity head below the energy line.

18. THANK YOU