fundamentals of flow in pipelines water...

Fundamentals of Flow in pipelines

Water Hammer

Dr. Ahmed ElmekawyFall 2018

Unsteady Flow• Fundamental of unsteady flow

• Practical approach

• Transitional wave principle

• Water hammer

• Water hammer effect

• Water hammer protection

• Unsteady flow equations

• Rigid water column theory

• Elastic Theory

Fundamentals of unsteady flow

• Steady flow: the value of all fluid properties, as well asflow properties at any fixed point, are independent of time.

• Unsteady flow: a fluid or flow property – or more - at a given point in space (locally) varies with time.

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Unsteady flow may be:

1. Non-Periodic flow: shut down, start up,closure processes for hydraulic components.

2. Periodic flow: periodic injection of the Air-Gasoline mixture in spark ignition engines.

3. Random flow: occurs in turbulent flow and is absent from laminar flow.

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Mathematically

For steady flow

For Quasi-steady flow

For unsteady flow

• Quasi-steady flow: the change of any propertyat any point with respect to time is so small orbehaves in slow rate and could be neglected.

• For simplicity of flow analysis, it could beassumed as steady (or quasi-steady) flow insome applications.

= 0.0t

0.0t

0.0t

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• Application in practice

1. Start up operations

(transition from zero velocity to steady state operation)

2. Shut down operations

(transition from steady state velocity to static equilibrium

state (v=0.0))

3. Hydraulic component closure (valves)

(transition from steady state operation to zero velocity in

small periods)

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Water Injection System

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Water Hammer

• is a pressure surge orwave resulting when afluid in motion is forcedto stop or changedirection suddenly(Momentum Change).

• Watercommonly

hammeroccurs when

a valve is closedsuddenly at an end of apipeline system, and apressure wavepropagates in the pipe.

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Water Hammer

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Practical approach

Aircraft tank valve

Aircraft tank valve closes in 2-5 seconds.

Ventbox

High level shut-off

If aircraft tank valve fails to close, vent line is designed to handle 50 psi

Vent Tank

Aircraft manifoldOverflow

Aircraft coupling maximum 120 psi

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Practical approach

• Necessary to protect aircraft fuel systems fromexcessive fuelling pressure and surge pressures.

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►When the generator of a water turbine is disconnected from a power network, the turbine speed starts to increase. Consequently, the turbine controller closes the inflow to the turbine, thus creating water hammer in the penstock.Water hammer effects in thepenstock are created by any changes in discharge through the turbine, caused by changes in the connected power network, by the operators, or by breakdowns.

Sometimes, the entire system

becomes unstable due to themutual influence of a turbine equipped with a controller and to an unsteady

flow in the penstock. In such case, even small variations in pressure in the

penstock may increase steadily and perilously.Flow in pipelines

Water hammer effect

Assume:

• The difference between the energy gradeline (EL) and the hydraulicgradeline (HGL) will be neglected

• Horizontal, constant-diameter pipe.

• Neglect friction.

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Illustration of Water Hammer

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Transitional wave principle

• Wave: is the substance reaction against anychange in an exerted phenomena and differsaccording to the substance itself.

Pressure wave → Substance reaction due to pressure change

Thermal wave → Substance reaction due to Thermal change

Surface wave → Substance reaction due to Height change

• Shock wave: is a produced wave due to verylarge change in the exerted phenomena in thesubstance.

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the effect of

Pressure waves

1. Pressure waves: Transmits pressure rise/increase.

the effect of2. Expansion waves: Transmitspressure drop/decrease.

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Water hammer effect

• Where

t : time sincevalve was closed

a : velocity of pressure wave

L : Length of the pipe

ΔH : increasingin pressure head

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Flow in pipelines


Open End

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Closed End

What is water hammer?

Water hammer (or hydraulic shock) is themomentary increase in pressure, which occurs in awater system when there is a sudden change ofdirection or velocity of the water.

When a rapidly closed valve suddenly stops waterflowing in a pipeline, pressure energy is transferredto the valve and pipe wall. Shock waves are set upwithin the system. Pressure waves travel backwarduntil encountering the next solid obstacle (orchange in density), then forward, then back again.The pressure wave’s velocity is equal to the speedof sound; therefore it “bangs” as it travels back andforth, until dissipated by friction losses.

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Anyone who has lived in an older house is familiarwith the “bang” that resounds through the pipeswhen a faucet is suddenly closed. This is an effectof water hammer.

A less severe form of hammer is called surge, aslow motion mass oscillation of water caused byinternal pressure fluctuations in the system. Thiscan be pictured as a slower “wave” of pressurebuilding within the system. Both water hammer andsurge are referred to as transient pressures.

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If not controlled, they both yield the same results:damage to pipes, fittings, and valves, causing leaksand shortening the life of the system. Neither thepipe nor the water will compress to absorb theshock.

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Investigating the Causes of Water Hammer

A water transport system’s operating conditions arealmost never at a steady state. Pressures and flowschange continually as pumps start and stop,demand fluctuates, and tank levels change. In

normal events, unforeseenaddition to these events, such as power outages and equipmentmalfunctions, can sharply change the operatingconditions of a system. Any change in liquid flowrate, regardless of the rate or magnitude of change,requires that the liquiddecelerated from its initial

be accelerated orflow velocity. Rapid

changes in flow rate require large forces that areseen as large pressures, which cause waterhammer.

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Entrained air or temperature changes of the wateralso can cause excess pressure in the water lines.Air trapped in the line will compress and will exertextra pressure on the water. Temperature changeswill actually cause the water to expand or contract,also affecting pressure. The maximum pressuresexperienced in a piping system are frequently theresult of vapor column separation, which is causedby the formation of void packets of vapor whenpressure drops so low that the liquid boils orvaporizes. Damaging pressures can occur whenthese cavities collapse.

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Summary

Water hammer refers to fluctuations caused by a suddenincrease or decrease in flow velocity. These pressurefluctuations can be severe enough to rupture a watermain. Potential water hammer problems should beconsidered when pipeline design is evaluated, and athorough surge analysis should be undertaken, in manyinstances, to avoid costly malfunctions in a distributionsystem. Every major system design change or operationchange—such as the demand for higher flow rates—should include consideration of potential water hammerproblems. This phenomenon and its significance to boththe design and operation of water systems is not widelyunderstood, as evidenced by the number and frequencyof failures caused by water hammer.

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Pressure and velocity waves in a single-conduit

frictionless pipeline following its sudden closure.

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Water hammer effect

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Flow in pipelines

Water hammer effect

Water hammer effect

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Water hammer effect

Example

Water hammer effect

● Pressure head at the valve

● Pressure head at the midpoint

● Pressure head at thereservoir

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The unsteady flow equations

Considering only the streamline direction, Newton’s second law gives

Where m = fluid particle mass, and s signifies the streamline direction.

Substituting the force components and mass from the figure into thisequation results in

dts s F = ma = m

dv

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s g dt

pA−

p +p

sA−W sin −sd =

W dv


After some manipulation, we end up with the one-dimensional Euler equation

−1 p

−z−

4=

1 dv

s s d g dt

Expanding the particle diameter to the size of the pipe cross-section and introduction the average velocity gives a more useful equation

−1 p

−z

−4 0 =

1 dv

s s D g dt

Where D is the pipe diameter and τ0 is not directly useful, we will substitute a

relation between τ0 and the Darcy-Weiscach friction factor ƒ. The result of

this substitution is

−1 p

−z

−f V 2

=1 dv

s s D 2g g dt

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Recognizing that z is a function only of s and represents the elevation abovesome datum of the pipe centerline, we can change the partial derivative to

a total derivation. Finally, the equation has the form

− 1 p −

dz−

f V 2

=1 dv

s ds D 2g g dt

This equation is valid for:

1- Compressible/ incompressible flow,

2- Steady/ unsteady flow,

3 Real/ Ideal flow,

4 Rigid and elastic pipe.

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• Assuming

1. Ideal flow

Neglect viscous force

2. Steady flow

− 1 p −

dz =

1 dv

s ds g dt

D 2g

2

−f V

= 0.0

dv = 0.0

dt

V = fn(s,t)

dt s dt t

dv =v

ds +v

dts t

dv

=v ds

+v

t

v 0.0

dv

= Vv

dt s

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= 0.01 p

+dz

+1 dv2

s ds 2g ds

p + Z + = E

2g

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• For incompressible flow (γ = constant)

v2

Euler equation forsteady ideal flow

Bernoulli’s equation

Rigid Water Column Theory

• 1- Neglect compressibility of the fluid i.e.,

ρ = Constant

• 2- neglect Elasticity of the pipe,

D = Constant

= 0.0

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1 p+

dz+

1 dv2

s ds g 2ds

Flow establishment in horizontal pipe

Because the pressure head p1/ω = constant = H0 and because p2/ ω = 0 for t>0

ds = 1 dV

dsL ds L 2gD L g dt

−

1 pds −

dzds −

fV2

L s

g dt

(dz/ds) = 0, and V is a function of time only, assume the ƒ-value in unsteady

flow is the same as for a steady flow at a velocity equal to the instantaneous

value.

p1 −p2 −

fL V 2 =

LdV

2gD

H −0

fL V 2 =

L dV

2gD g dt

0

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H −g

Integration is performed by separating the variables to form

dt =L

dV


The integration gives the following equation for the time necessary toaccelerate the flow to given velocity V

Recognizing thatsteady state velocity, the equation for t becomes

fL

LD fL

−V

+V

t =2gDH0

2gDH0

ln2gfH0

t =LV0 ln

V0 +V

2gH0 V0 −V

V0 = 2gH0 D / fL , the

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gH0

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• It is important to note that as steady flow isapproached, V → V0 and as a consequence t → ∞.

Of course this answer is unacceptable so wepropose that when V = 0.99 V0, we haveessentially steady flow. With this interpretation,

t = 2.65LV0


• When the valve isclosed pressure iseverywhere equalto H0.

• When the valve issuddenly opened.The pressure atthe valve dropsinstantly to zeroand the fluidbegins toaccelerate.

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Example.1

A horizontal pipe 24” inside diameter, 10,000 ftlong leaves a reservoir 100 ft below surface andterminates with a closed valve. If the valve openssuddenly. How long would the velocity takes toreach 99% of its final value, neglecting minorlosses valve. Friction factor of 0.018 is to beassumed constant during the acceleration phase

• Given:

d = 24” = 2 ft L = 104 ft Ho = 100 ft F = 0.018= const

• Required:

t for a velocity of 0.99Vo

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Example.1

• Solution

flo

2gdHo

0.018104

232.22100= 8.45 ft /s=

V =

t =lVo ln

Vo +V

2gHo Vo −V

ln232.2100 8.46 (1−0.99)

104 8.46 8.46 (1+0.99)t =

t = 70 second

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Water Hummer Protection

Using Accumulators and Air Chambers

Flow in pipelines

Water Hummer Protection

1. Automatically controlled valves which close slowly

2. Pumps: Increasing the flow slowly during startup and shut down

3. Using Accumulators and Air Chambers

Flow in pipelines

fundamentals of flow in pipelines water...

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