GOVERNMENT ENGINEERING COLLEGE-BHUJ LAMINAR FLOW IN PIPES 

- UNDER GUIDANCE OF … PROF. DIPEN V CHAUHAN DEPTT. OF CHEMICAL ENGINEERING,BHUJ A PRESENTATION MADE BY- KUMAR SATYAM SHELADAYA PIYUSH PATEL AKSHAY

WHAT IS LAMINAR FLOW? At low velocities, fluids tend to flow without lateral mixing, and adjacent layers slide past each other as playing cards do. There are neither cross- currents nor eddies. This regime is called laminar flow. At higher velocities turbulence appears and eddies form leads to lateral mixing

WHAT IS VISCOSITY? In a Newtonian fluid, the shear stress is proportional to the shear rate, and the proportionality constant is called the viscosity

VISCOSITY IN LIQUIDS The viscosities of liquids are much greater than those of gases at the same temperature. Molecules in liquids move very short distances between collisions, and most momentum transfer occurs as molecules in a velocity gradient slide past one another. The viscosity generally increases with molecular weight and decreases rapidly with increasing temperature. The main effect of temperature change comes not from the increase of average velocity, as in gases, but from the slight expansion of the liquid, which makes it easier for the molecules to slide past one another.

THE VIDEO PROVIDED BELOW THE PASSING OF LIQUID SURFACES OVER EACH OTHER, HERE THE LIQUIDS USED(CORN SYRUP AND DYE) DOES NOT MIX IN THEMSELVES EVEN AFTER THOROUGH AGITATION CLICK ON THE BOX BELOW TO PLAY THE VIDEO

Transition at R of 2000 LAMINAR AND TURBULENT FLOWS Reynolds apparatus damping inertia

BOUNDARY LAYER GROWTH: TRANSITION LENGTH Pipe Entrance What does the water near the pipeline wall experience? _________________________ Why does the water in the center of the pipeline speed up? _________________________ v v Drag or shear Conservation of mass Non-Uniform Flow v

LAMINAR, INCOMPRESSIBLE, STEADY, UNIFORM FLOW Between Parallel Plates Through circular tubes Hagen-Poiseuille Equation Approach Because it is laminar flow the shear forces can be easily quantified Velocity profiles can be determined from a force balance Don’t need to use dimensional analysis

LAMINAR FLOW THROUGH CIRCULAR TUBES Different geometry, same equation development (see Streeter, et al. p 268) Apply equation of motion to cylindrical sleeve (use cylindrical coordinates)

LAMINAR FLOW THROUGH CIRCULAR TUBES: EQUATIONS Velocity distribution is paraboloid of revolution therefore _____________ _____________ Q = VA = Max velocity when r = 0 average velocity (V) is 1/2 u max Vpa2Vpa2 a is radius of the tube

LAMINAR FLOW THROUGH CIRCULAR TUBES: DIAGRAM Velocity Shear True for Laminar or Turbulent flow Shear at the wall Laminar flow

THE HAGEN-POISEUILLE EQUATION cv pipe flow Constant cross section Laminar pipe flow equations CV equations! h or z

EXAMPLE PIPE FLOW PROBLEM D=20 cm L=500 m valve 100 m Find the discharge, Q. Describe the process in terms of energy! cs 1 cs 2

TURBULENCE A characteristic of the flow. How can we characterize turbulence? intensity of the velocity fluctuations size of the fluctuations (length scale) mean velocity mean velocity instantaneous velocity instantaneous velocity fluctuation velocity fluctuation 

VELOCITY DISTRIBUTIONS Turbulence causes transfer of momentum from center of pipe to fluid closer to the pipe wall. Mixing of fluid (transfer of momentum) causes the central region of the pipe to have relatively _______velocity (compared to laminar flow) Close to the pipe wall eddies are smaller (size proportional to distance to the boundary) constant

TURBULENT FLOW VELOCITY PROFILE Length scale and velocity of “large” eddies y Turbulent shear is from momentum transfer h = eddy viscosity Dimensional analysis

TURBULENT FLOW VELOCITY PROFILE Size of the eddies __________ as we move further from the wall. increases k = 0.4 (from experiments)

PIPE FLOW ENERGY LOSSES Horizontal pipe Dimensional Analysis Darcy-Weisbach equation

FRICTION FACTOR : MAJOR LOSSES Laminar flow Turbulent (Smooth, Transition, Rough) Colebrook Formula Moody diagram

LAMINAR FLOW FRICTION FACTOR Slope of ___ on log-log plot Hagen-Poiseuille Darcy-Weisbach

SMOOTH, TRANSITION, ROUGH TURBULENT FLOW Hydraulically smooth pipe law (von Karman, 1930) Rough pipe law (von Karman, 1930) Transition function for both smooth and rough pipe laws (Colebrook) (used to draw the Moody diagram)

MOODY DIAGRAM E+031E+041E+051E+061E+071E+08 R friction factor laminar smooth

MINOR LOSSES We previously obtained losses through an expansion using conservation of energy, momentum, and mass Most minor losses can not be obtained analytically, so they must be measured Minor losses are often expressed as a loss coefficient, K, times the velocity head. High R

HEAD LOSS DUE TO GRADUAL EXPANSION (DIFFUSOR)  diffusor angle (  ) KEKE

SUDDEN CONTRACTION losses are reduced with a gradual contraction V1V1 V2V2 flow separation

SUDDEN CONTRACTION A 2 /A 1 CcCc

ENTRANCE LOSSES Losses can be reduced by accelerating the flow gradually and eliminating the vena contracta

HEAD LOSS IN BENDS Head loss is a function of the ratio of the bend radius to the pipe diameter (R/D) Velocity distribution returns to normal several pipe diameters downstream High pressure Low pressure Possible separation from wall D K b varies from R

HEAD LOSS IN VALVES Function of valve type and valve position The complex flow path through valves can result in high head loss (of course, one of the purposes of a valve is to create head loss when it is not fully open)

EXAMPLE: MINOR AND MAJOR LOSSES Find the maximum dependable flow between the reservoirs for a water temperature range of 4ºC to 20ºC. Water 2500 m of 8” PVC pipe 1500 m of 6” PVC pipe Gate valve wide open Standard elbows Reentrant pipes at reservoirs 25 m elevation difference in reservoir water levels Sudden contraction

PIPE FLOW SUMMARY (1) Shear increases _________ with distance from the center of the pipe (for both laminar and turbulent flow) Laminar flow losses and velocity distributions can be derived based on momentum and energy conservation Turbulent flow losses and velocity distributions require ___________ results linearly experimental

PIPE FLOW SUMMARY (2) Energy equation left us with the elusive head loss term Dimensional analysis gave us the form of the head loss term (pressure coefficient) Experiments gave us the relationship between the pressure coefficient and the geometric parameters and the Reynolds number (results summarized on Moody diagram)

PIPE FLOW SUMMARY (3) Dimensionally correct equations fit to the empirical results can be incorporated into computer or calculator solution techniques Minor losses are obtained from the pressure coefficient based on the fact that the pressure coefficient is _______ at high Reynolds numbers Solutions for discharge or pipe diameter often require iterative or computer solutions constant

PIPES ARE EVERYWHERE! Owner: City of Hammond, IN Project: Water Main Relocation Pipe Size: 54"

PIPES ARE EVERYWHERE! DRAINAGE PIPES

PIPES

PIPES ARE EVERYWHERE! WATER MAINS