Flow in Pipes - Fluids Mechanic

7/23/2019 Flow in Pipes - Fluids Mechanic

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FC-CIV MECAFLUI:Fluid Mechanics

Session 18:

Flow in Pipes (Part I)

Eusebio Ingol Blanco, Ph.D.

Civil Engineering Program, San Ignacio de LoyolaUniversity


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Objective

Understand the laminar and turbulent flowin pipes.

Calculate the major and minor losses

associated with pipe flow in pipingnetworks


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Motivation

Internal flows through pipes, elbows, tees,

valves, etc., as in this oil refinery, are found

in nearly every industry.

Water supply and sanitation


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Introduction

Liquid or gas flow through pipes or ducts is commonly

used in heating and cooling applications and fluiddistribution network.

The fluid in such applications is usually forced to flow by a

fan or pump through a flow section.

Particular attention to friction,which is related to thepressure drop and head loss.

The pressure drop is then used to determine the pumping

power requirement


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Introduction

Average velocity Vavgis defined as theaverage speed through a cross section. For

fully developed laminar pipe flow, Vavgis half

of the maximum velocity.

The value of the average velocity Vavg at some

streamwise cross-section is determined fromthe requirement that the conservation of mass

principle be satisfied

The average velocity

for incompressible

flow in a circular pipeof radiusR


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Laminar and Turbulent Flow

Laminar:Smooth streamlines and highlyordered motion.

Turbulent:Velocity fluctuations and highly

disordered motion.

Transition:The flow fluctuates between

laminar and turbulent flows.Most flows encountered in practice are

turbulent.

The behavior of colored fluid injected into theflow in laminar and turbulent flows in a pipe.


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Reynolds Number

The transition from laminar to turbulent flow depends on

the geometry, surface roughness, flow velocity, surfacetemperature, and type of fluid.

The flow regime depends mainly on the ratio of inertial

forcesto viscous forces(Reynolds number).

Critical Reynolds number, Recr: The Reynolds number at

which the flow becomes turbulent.

The value of the critical Reynolds number is different for

different geometries and flow conditions.


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Reynolds Number

For flow through noncircular

pipes, the Reynolds number is

based on the hydraulic diameter

For flow in a circular pipe:


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The Entrance RegionVelocity boundary layer:The region of the flow in which the effects

of the viscous shearing forces caused by fluid viscosity are felt.

Boundary layer region:The viscous effects and the velocity changes

are significant.

Irrotational (core) flow region:The frictional effects are negligible

and the velocity remains essentially constant in the radial direction.

The development of the velocity boundary layer in a pipe..


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Pressure and wall shear stress

The variation of wall shear stress in the flow direction for flow in a pipe

from the entrance region into the fully developed region.

The pressure drop is higher in the entrance regions of a pipe,

and the effect of the entrance region is always to increase the

average friction factor for the entire pipe.


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Entry Length

The hydrodynamic entry length is usually taken to be the distance fromthe pipe entrance to where the wall shearstress (and thus the friction

factor) reaches within about 2 percent of the fully developed value.

hydrodynamic

entry length for

laminar flow

hydrodynamic

entry length for

turbulent flow

hydrodynamic entry

length for turbulent flow,

an approximation


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Laminar Flow in PipesWe consider steady, laminar, incompressible flow of a fluid with constant properties in

the fully developed region of a straight circular pipe.

Free-body diagram of a ring-shaped

differential fluid element of radius r,thickness dr, and length dx oriented coaxially

with a horizontal pipe in fully developed

laminar flow.


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Laminar Flow in Pipes

Boundary conditions

Maximim velocity

at centerline (r = 0)

Velocity

profile

Average velocity


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Pressure Drop and Head Loss

A pressure drop due to viscous effects represents an irreversible pressure

loss, and it is calledpressure loss PL.

pressure loss for all

types of fully developedinternal flows

dynamic

pressure

Circular pipe, laminar

DarcyWeisbach friction

factor

In laminar flow, the friction

factor is a function of the

Reynolds number only and is

independent of the roughness of

the pipe surface.

The head loss represents theadditional height that the fluid

needs to be raised by a pump in

order to overcome the frictional

losses in the pipe.

Substituting this eq. into Vavg expression:, the pressure drop is expressed as:


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The relation for pressure loss (and head loss) is one of the most

general relations in fluid mechanics, and it is valid for laminar

or turbulent flows, circular or noncircular pipes, and pipes with

smooth or rough surfaces.


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The required pumping power to overcome the pressure loss in determined :

Horizontal pipe

Poiseuilleslaw

The pumping power requirement for a laminar flow

piping system can be reduced by a factor of 16 by

doubling the pipe diameter.

For a specified flow rate, the pressure drop and thus the

required pumping power is proportional to the length of

the pipe and the viscosity of the fluid, but it is inversely

proportional to the fourth power of the diameterof the

pipe.


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The pressure drop P equals the pressure loss PLin the case of a

horizontal pipe, but this is not the case for inclined pipes or pipeswith variable cross-sectional area.

This can be demonstrated by writing the energy equation for steady,

incompressible one-dimensional flow in terms of heads as


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Effect of Gravity on Velocity and Flow Rate in

Laminar Flow


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Laminar Flow in no Circular Pipes


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Example 8-1


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Example 8-1

Solution:

E l 8 1


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Example 8-1


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Example 8-2


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Example 8-2


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Example 8-2


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Problem 8-31

Water at 10C ( = 999.7 kg/m3 and = 1.307 x

(10)^-3 kg/m s) is flowing steadily in a 0.20-cm-diameter, 15-m-long pipe at an average velocity of 1.2

m/s. Determine:

(a) the pressure drop, (b) the head loss, and (c) the

pumping power requirement to overcome this pressure

drop.


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Problem 8-35

The velocity profile in fully developed laminar flow

in a circular pipe of inner radiusR = 2 cm, in m/s, isgivenby u(r) = 4(1 - r^2/R^2). Determine the

average and maximum velocities in the pipe and the

volume flow rate.


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Problem 8-137E

The velocity profile in a fully developed laminar flow of water

at 40F in a 80-ft-long horizontal circular pipe, in ft/s, is given

by u(r) = 0.8(1 625r^2), where r is the radial distance from the

centerline of the pipe in ft. Determine:

(a) the volume flow rate of water through the pipe, (b) the

pressure drop across the pipe, and (c) the useful pumping

power required to overcome this pressure drop.Assume that the pipe is inclined120 from the horizontal and

the flow is uphill


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Summary

Flow in Pipes: Laminar and turbulentflows.

The entrance region

Laminar flow in pipes: Pressure drop and

head loss Effect of gravity on velocity and flow

rate

Examples


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Homework

Study sections: 8-1, 8-2, 8-3, 8-4

Homework 7 is going to be posted soon

Flow in Pipes - Fluids Mechanic

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