NOTES

ANALYSIS OF FLOW IN PIPE

INTRODUCTION

There are 3 types of flow in pipe:

i) Turbulent- Velocity fluctuations and highly disordered motion. 

ii) Transitional - The flow fluctuates between laminar and turbulent flows.

iii) Laminar- Smooth streamlines and highly ordered motion.

FLOWS IN PIPE

REYNOLDS NUMBER

-Reynolds Number - A dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations.

-Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces (vρ) to viscous forces (μ / L)

      SIMPLE REYNOLD EXPERIMENT

            

        Transition : The fluctuation between laminar and turbulent flows.

 REYNOLD'S NUMBER(Re)

-The transition from laminar to turbulent flow depends on the geometry, surface roughness, flow velocity, surface temperature, and type of fluid, among other things.

-The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number, Recr.

FLOW IN PIPE

                        

ratio of inertial forces to viscous forces acting on a fluid element.

FRICTION IN PIPE

-When fluid flows in pipe conduit, shear stress will be occured

-Velocity in pipe will be decreased because of energy loss that can be measured by pressure differences.

-Reynold also predict the friction,hf  in pipe by measuring the differences of pressure with known length, L

TOTALS HEADS MEASURED

FRICTION IN NON CIRCULAR CONDUITS

FRICTION IN CIRCULAR CONDUITS

-Friction in circular conduits when flowing full

--->The equation is known as the pipe-friction equation and Darcy-Weisbach equation

FORMULA HAGEN POISEUILLE

-For laminar flow only

-The loss of head is proportional to the first power of velocity

-The friction is independent of the roughness of the pipe but depends on viscosity and density.

FORMULA DARCY-WEISBACH

FRICTION FACTOR

Friction factor for laminar flow is:

where :                    
v: dynamic viscosity
  D: diameter              
V: velocity              
R: Reynolds Number

RELATIVE ROUGHNESS, ε

ε: relative roughness

e: pipe roughness

D: diameter

MOODY CHART

-used for both BG and  SI unit systems
-is a graph in non-dimensional form that relates the Darcy-Weisbach friction factor, Reynolds number and relative roughness for fully developed flow in a circular pipe. 
-The SI based friction factor is four times larger than the Imperial based    friction factor.

MOODY CHART

Moody chart divided into 4 parts
- laminar
-critical                     : values uncertain where flow either laminar or turbulent
-transition                 : f is a function of both R and є
-complete turbulent  : f is independent of R and depend solely upon the relative roughness.

MINOR LOSSES IN PIPE

-Losses caused by local disturbances of the flow in the conduit such as fittings, bends, valves, etc. 
-Losses are proportional to – velocity of flow, geometry of device

-The value of K is typically provided for various devices. 
-Energy lost – units – N.m/N or lb-ft/lb 
-K - loss factor - has no units (dimensionless) 

It also can be represent by being equivalent to a certain length of straight pipe,expressed in terms of number of pipe diameter,N

LOSS OF HEAD AT ENTRANCE

-Happen when the fluid from reservoir enter the pipe.
-At point c velocity is maximum and minimum pressure

-Vena contracta is the point in a fluid stream where the diameter of the stream is the least, and fluid velocity is at its maximum, such as in the case of a stream issuing out of a nozzle, (orifice). It is a place where the cross section area is minimum.

-The maximum contraction takes place at a section slightly downstream of the orifice, where the jet is more or less horizontal.

LOSS OF HEAD AT SUBMERGED DISCHARGED

-Loss of head at submerged discharge:
When a fluid with a velocity V is discharged from the end of a pipe into a closed tank which is so large that the velocity within it is negligible, the entire kinetic energy is dissipated. 

-It occur when a water with velocity is discharged into a body of water moving away in channel
-Pressure distribution at section cf is given by

Equation of streamline is:

LOSS DUE TO CONTRACTION

SUDDEN CONTRACTION

-There is a marked drop in pressure due to increase in velocity and to loss of energy in turbulence. 

-At section C – rise in pressure because the streamlines are curving

-The pressure distribution is varied along section B to C. 

-At section C to E, the conditions are similar to those described as     for entrance. 

-D2/D1 = 0 for the entrance loss. 

-Head loss for sudden contraction is:

GRADUAL CONTRACTION

LOSS DUE TO EXPANSION

SUDDEN EXPANSION

-There is rise in pressure because of the decrease in velocity.

-At C to F – excessive turbulence in the flow.

-Then, loss of head due to sudden enlargement is 

GRADUAL EXPANSION

-Gradual expansion – i.e. diffuser 
-To minimize the loss accompanying reduction in velocity a diffuser can be used.
-The loss due to a gradual enlargement is

LOSS IN PIPE FITTING

The head loss in pipe fittings can be express as

The value of k is depends on L/D

LOSS IN ELBOWS AND BENDS

-values of kb for 90 bends, varying with bend radius and pipe roughness