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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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