SOE2156: Fluids Lecture 2

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1 and Pipe Turbulence and Pipe SOE2156: Fluids Lecture 2

2 and Pipe Energy form : p U2 + gz = constant (along a streamline) g, the specic weight Alternatively, divide by g { head loss form : p + U 2 + z = constant (along a streamline) g 2g

3 and Pipe Assumptions : 1 Viscous eects negligable 2 steady 3 Equation applies along streamline 4 Fluid is incompressible 5 No energy added/removed However we can often relax some of these assumptions : : :

4 and Pipe Assumptions : 1 Viscous eects negligable 2 steady 3 Equation applies along streamline 4 Fluid is incompressible 5 No energy added/removed However we can often relax some of these assumptions : : : p + U 2 + g 2g z + H L = constant (along a pipe)

5 and Pipe Classic experiment : U 1 U 2 U 3 P a U 1 U 2 U 1 U 3 Piezometer tube Piezometer tube measures piezometric head p g + z (Piezometer tube has its end parallel to the ow)

6 and Pipe Classic experiment : P a U 1 U 2 U 3 U < 1 U 2 U 1 = U 3 Piezometer tube Piezometer tube measures piezometric head p g + z (Piezometer tube has its end parallel to the ow)

7 and Pipe Classic experiment : P a U 1 U 2 U 3 U < 1 U 2 U 1 = U 3 Piezometer tube Piezometer tube measures piezometric head p g + z (Piezometer tube has its end parallel to the ow)

8 and Pipe Classic experiment : HGL P a Piezometer tube U 1 U 2 U 3 U < 1 U 2 U 1 = U 3 Piezometer tube measures piezometric head p g + z (Piezometer tube has its end parallel to the ow) Line drawn through the liquid levels in the piezometers { hydraulic grade line (HGL) or piezometric line.

9 and Pipe A pitot tube points into the ow, and so measures the kinetic energy as well : 0 1 Line drawn through pitot tube liquid surfaces { energy line (EL)

10 and Pipe A pitot tube points into the ow, and so measures the kinetic energy as well : 0 p + V 2 g 2g 1 0 = p 1 g + 0 Line drawn through pitot tube liquid surfaces { energy line (EL)

11 and Pipe Distinguish between absolute and relative to atmospheric { gauge. Most devices measure gauge. U-tube manometer p A = p a + m gh 2 gh 1 h P A 2 h 1

12 and Pipe a h b Dierential manometer p = g(b a) + hg( m ) Also { piezzometric techniques

13 and Pipe Pitot-static tube { measures uid velocity by comparing static and dynamic s Probe has to point into ow. More complex arrangements { 3 velocity components.

14 and Pipe Other velocity measurement techniques : Propellar meter Hot wire probe { heat loss from heated probe depends on u : measure temperature Particle Image Velocimetry (PIV) { seed ow with particles, iluminate with laser, successive photos give velocity vectors Laser Doppler Anemometry (LDA/LDV) { seed ow with particles, bounce laser beam o, measure doppler shift. Weirs, umes (more volume ow than velocity)

15 and Pipe Often we want to see the ow pattern { visualisation. In experiments this usually means tracing the paths taken by elements of the uid { usually by marking with a dye. For computer simulation it indicates any means of displaying the ow variables (p, u, T etc) visually { vectors, contour lines...

16 and Pipe Distinguish : Pathlines { path mapped out by a specic, marked element of uid Streaklines { line created by continuous release of dye from a point Streamlines { line whose tangent at each point gives the velocity vector For simple cases (particularly steady ow) these may all be the same. For complicated cases (unsteady ow) they may be markedly dierent.

17 and Pipe in pipes Osbourne experiment { Dye injector Control valve Water Visualise ow in circular pipe at dierent ow rates : A. Low ow rate { smooth, orderly ow { particles of uid retain same relative positions. B. High ow rate { ow no longer orderly { particles of uid mixed up { (almost) random uctuations in velocity,.

18 and Pipe Distinguish between two types of ow { laminar (case A) and turbulent (case B). Properties of the ow (in pipes and elsewhere) are markedly dierent in the two cases! Above a particular ow speed U crit the ow in the pipe is turbulent, below it is laminar. This critical ow speed depends on : Size (diameter d) of the pipe Viscosity (kinematic or dynamic ) of the uid.

19 and Pipe number However if we calculate the number Re = Ud then the ow is turbulent for Re > 2300, and laminar for Re < The number is a very important parameter in uid dynamics. For any ow, we can evaluate the number as a velocity a length scale Re = the kinematic viscosity

20 and Pipe If Re > Re crit (value depends on case) { the ow will be turbulent. If Re identical for two geometrically similar ows { the ow patterns will be the same.

UNIT I FLUID PROPERTIES AND FLUID STATICS

UNIT I FLUID PROPERTIES AND FLUID STATICS SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : FM & HM (16CE112) Year & Sem: II-B.Tech & I-Sem Course & Branch: B.Tech