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

1. Subject Name: FLUID MECHANICS Subject Code:10ME36B Prepared By: PUNITH R Department: AE Date: 09-09-2014

2. Laminar 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 • 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