Water Hammer

WATER HAMMER

MUHAMMAD AKBAR2005-CE-12

DEFINATION

Whenever, the velocity in pipe line is reduced instantaneously or in a very short time, a sudden increase in pressure takes place. This sudden rise in pressure in a pipe due to stoppage of the flow is known as WATER HAMMER OR HAMMER BLOW/WATER HAMMER PRESSURE.Terminology “Water Hammer” is perhaps misleading since this can occur in any liquid.

EFFECTS OF WATER HAMMER

• PRODUCE MORE PRESSURE IN PIPE• PRODUCE SHOCK WAVES• HAMMERING NOISE• CAN DAMAGE TO THE PIPE

DAMAGE CAUSED BY WATER HAMMER

DAMAGE CAUSED BY WATER HAMMER

VELOCITY OF PRESSURE WAVE

Velocity of pressure wave is denoted by ″C″The velocity of pressure wave in Rigid pipe is given as

Where,• Ev = volume modulus of the liquid in Pascal• Ρ = mass density of the liquid in Kg/m3

for water typical value of Ev = 2.07 x 106

KN/m2

VALUES OF

VALUES OF

VELOCITY OF PRESSURE WAVE

The velocity of pressure wave in elastic pipe is given as

Where,D = Diameter of pipet = thickness of pipeE = Modulus of elasticity of pipe material

Elastic pipe has less velocity of pressure wave than rigid pipe.

Example:

For rigid pipe,

Now for elastic pipe,

Consider,Dia of pipe = 15 cmPipe thickness, t = 1.5 cmMaximum pressure rise = 1700 KN/m2

Ev = 2.06 x 106 KpaE = 117 x 106 Kpa

Hence,

Equation for Water Hammer Pressure

If the time for closing the valve (T) is assumed to be zero the valve closure is called instantaneous valve closure.

Equation for Water Hammer Pressure

Let “dv” is change in velocity in time “dt” as the valve is closed abruptly. In time dt an element of liquid, of length “Cdt” is brought to rest.

The mass of the liquid compressed against the valve and comes to rest in time “dt” will be,

Multiplying both sides by ‘a’

Equation for Water Hammer Pressure

WATER HAMMER AND PRESSURE INTENSITY IN

FRICTIONLESS PIPE

DEVELOPMENT OF WATER HAMMER PRESSURE &

PRESSURE INTENSITY AT POINT “B”

INSTANTANEOUS VALVE CLOSURE •If the time for closing the valve ″T″ is assumed to zero, the valve closure is called Instantaneous valve closure.•T is the time for closing the valve..Consider a pipe of length ″L″ leading from a reservoir and terminating in a valve at its downstream. When the valve is Instantaneous closed a pressure of magnitude ″Ph″ is formed and moves up with velocity ″C″. The wave undergoes reflections at the reservoir end as well as at the valve.

CASE 1

For t = 0, the pressure profile is steady, which is shown by the pressure head curve running horizontally because of the assumed lack of friction.

Comment: Due to instantaneous closure of valve t=0,so Ph=0.

CASE 2The sudden closure of the gate valve at the downstream end of the pipeline causes a pulse of high pressure h; and the pipe wall is stretched. The pressure wave generated runs in the opposite direction to the steady-state direction of the flow at the speed of sound and is accompanied by a reduction of the flow velocity to v = 0 in the high pressure zone. Expansion will take place in pipe due to positive pressure.

Comment: WHP attains its half maximum +ve value up to the time L /2c.

CASE 3 At t = 1/2Tr the pressure wave has arrived at the reservoir. As

the reservoir pressure p = constant, there is an unbalanced condition at this point. With a change of sign, the pressure wave is reflected in the opposite direction. The flow velocity changes sign and is now headed in the direction of the reservoir. Expansion will take place in the pipe and

Comment:WHP attains maximum +ve value and remains constant up to L /c time.

CASE 4A relief wave with a head of h travels downstream towards the gate valve and reaches it at a time t = Tr. It is accompanied by a change of velocity to the value -V0. Positive pressure produces towards valve and

Comment: Value of WHP decreases to half for next t=L/2c .

CASE 5

Upon arrival at the closed gate valve, the half cycle is completed and

Comment: Value of WHP decreases to zero and remains zero up to t= 2L /c .

CASE 6The low pressure wave –h travels upstream to the reservoir in a time Tr < t < 3/2Tr, and at the same time, v adopts the value v = 0 and contraction will take place in the pipe , also

Comment: -ve pressure is produced at t= 5L/2c and its value is half to the maximum –ve pressure.

CASE 7The reservoir is reached in a time t = 3/2Tr, and the pressure resumes the reservoir’s pressure head and contraction will take place in the complete pipe, also

Comment: WHP attains maximum –ve pressure value and remains constant up to t= 3L /c .

CASE 8In a period of time 3/2Tr < t < 2Tr , the wave of increased pressure originating from the reservoir runs back to the gate valve and v once again adopts the value v0 and

Comment: during t=7L /2c its value decreases to half of the maximum –ve pressure .

CASE 9

At t = 2Tr , conditions are exactly the same as at the instant of closure t = 0, and the whole process starts over again.

Comment: value of WHP become zero due to the completion of cycle at t= 4L/c.

DEVELOPMENT OF WATER HAMMER PRESSURE & PRESSURE INTENSITY

AT POINT “M”

COMMENTSCASE 1:As the valve is not yet closed, so at

t=0,Ph=0.

CASE 2:At time L/2c ,just before point M ,water hammer pressure intensity is zero.

CASE 3:At time L/c , the pressure is maximum.

COMMENTSCASE 4: At time 3L /2c ,pressure intensity is

constant for a very short time, then decreases to zero.

CASE 5: For next time L/2c i.eat t=2L/c ,pressure intensity remains zero.

CASE 6: Up to t =5L /2c WH pressure is just before the point “M” , so pressure is zero

COMMENTSCASE 7: At t=3L/c maximum –ve pressure is

produced and for a short time its value is zero.

CASE 8:During next t=L /2c WH pressure value remains constant for a while and then decreases to zero.

CASE 9: At t=4L/c the cycle is completed and pressure is zero.

DEVELOPMENT OF WATER HAMMER PRESSURE & PRESSURE INTENSITY

AT POINT “A”

COMMENTSCASE 1: At t=0 valve is not yet closed ,so Ph =0

CASE 2: At t= L/2c WHP is not reached at point “A” ,so Ph=0.

CASE 3: Maximum +ve WHP produces for very short time at t=L /c.

COMMENTSCASE 4: At t=3L /2c WHP is zero.

CASE 5: At t= 2L/c half cycle is completed and Ph=0.

CASE 6:Up to t=5L /2c –ve pressure is not yet reached at point “A” , so WHP is zero.

COMMENTSCASE 7: At t=3L /c maximum –ve pressure is

produced and for a short time.

CASE 8:During next t=L /2c WH pressure value again becomes zero.

CASE 9: At t=4L/c the cycle is completed and WHP is zero.

DEVELOPMENT OF WATER HAMMER AND PRESSURE

INTENSITY IN FRICTION PIPES

• Consider a pipe affected by both friction and damping.

• Now consider the real case where the valve is closed in a finite time which is more than zero but less than 2L/c.

• The pressure wave travels from point B (valve) towards the reservoir.

• When it reaches point B, the water comes to rest.

WATER HAMMER PRESSURE AND PRESSURE INTENSITY AT

POINT “B”

COMMENTSCase 1:At t=0 the valve is not yet closed ,so

Ph=0

Case 2: “ 0 < t < L/2c ” is the real time to close the valve , so at this time Ph=0

Case 3:At t= L/2c WHP produces and attains its maximum +ve value.

COMMENTS

Case 4: After t=L/2c WHP increases linearly due to friction up to t=L /c.

Case 5: Pressure decreases up to t=3L /2c .

Case 6: Pressure continues to decrease up to t=2L /c and then becomes zero.

COMMENTS

Case 7: After t=2L/c WHP attains –ve value up to t=5L /2c.

Case 8: WHP attains its maximum –ve value at t= 3L/c.

Case 9: At t=7L /2c pressure increases.

CommentCase 10: At t= 4L /c one cycle is completed and

Ph=0.

WATER HAMMER PRESSURE AND PRESSURE INTENSITY

AT POINT “M”

COMMENTSCase 1:At t=0 the valve is not yet closed ,so

Ph=0

Case 2: “ 0 < t < L/2c ” is the real time to close the valve , so at this time Ph=0

Case 3:At t= L/2c ,Ph becomes zero because it is just before point “M”.

COMMENTS

Case 4: At t=L /c WHP attains its maximum +ve value at point “M”.

Case 5: At t=3L /2c WHP reduces and becomes zero.

Case 6: At t=2L /c half cycle is completed and WHP is zero.

COMMENTS

Case 7: There is no change in pressure during t=5L /2c.

Case 8: At t=3L/c pressure has its maximum –ve value.

Case 9: WHP increases and becomes zero at t=7L /2c.

COMMENTCase 10: One cycle is completed and WHP is

zero at t=4L /c.

WATER HAMMER PRESSURE AT PRESSURE INTENSITY

AT POINT “A”

COMMENTSCase 1:At t=0 the valve is not yet closed ,so

Ph=0

Case 2: “ 0 < t < L/2c ” is the real time to close the valve , so at this time Ph=0

Case 3:At t= L/2c ,Ph becomes zero because it is before point “A”

COMMENTSCase 4: At t=L /c WHP attains its maximum +ve

value for a very short time and then become zero.

Case 5: At t=3L /2c WHP is zero.

Case 6: At t= 2L /c half cycle is completed and WHP is zero.

COMMENTSCase 7: At t=5L /2c WHP is zero because it is

before point “A”.

Case 8: At t=3L /c WHP attains its maximum –ve value for a very short time and then

becomes to zero.

Case 9: At t= 7L /2c WHP is zero.

COMMENTCase 10: One cycle is completed at t=4L /c and

Ph=0.

RAPID VALVE CLOSURE•If the time for closing the valve ″T″ is more than Zero but less than ″2L/C ″ the valve closure is called as Rapid Valve Closure.•T≤2L/C•The maximum pressure rise is still the same as for instantaneous closure. i.e.

SLOW VALVE CLOSURE

•If the time for closing the valve is greater than ″2L/C″ the valve closure is called as slow valve closure.•T › 2L/C•In this case the maximum pressure rise is less than in the preceding. Thus the water hammer pressure for slow valve closure when, T=2L/C is given approximately;

DESIGN OF PIPE THICKNESS

•The water hammer pressure Ph will be above and over steady state pressure in pipe.•Ps (referred commonly as static pressure). Hence, the pipe will have to withstand a total pressure Pt given by

•The stress in the pipe wall is given by the thin cylinder formula.

Where,t = thickness of the pipe wallD = diameter of the pipe

For design, stress should be less than working stress of the pipe material.

The minimum thickness of the pipe wall is,

For steel normal working stress is 100 MPa.

Method for controlling Water Hammer

1. Slow valve closure2. Pressure relief valve3. Surge tank4. Compressor type air vessel

SLOW VALVE CLOSUREValve should be closed to avoid the danger of production of high water hammer pressure.

PRESSURE RELIEF VALVESA pressure relief valve is provided at some distance from the end valve. When excess pressure is produced in the pipe due to sudden closure of end valve, pressure relief valve is automatically opened to allow the escape of water so controlling the excess pressure in the pipe.

SURGE TANKSA simple surge tank is a vertical stand pipe connected to the pipe line as close to the valve as possible.when the valve is suddenly closed, water rises in the surge tank. The water surface in the tank will then fluctuate up and down. The section of pipe upstream of the surge tank is thus protected from high water hammer pressure.So only the part of the pipe downstream of the surge tank is to be designed for high water hammer pressure.

Surge tanks

Schematic layout of a compressor-type air vessel. To avoid excessive pressures on return of the vessel water

vessel water,

Practical Application of Water Hammer

Problem

Water from a reservoir flowing through a rigid pipe 15 cm diameter, with a velocity of 2.44 m/s, is completely stopped by a valve situated at 1067 m from reservoir. Determine the maximum rise in pressure when valve closure takes place.1. 1sec.2. 5 sec.

Ev for water 2.06 x 106 KPa.

Solution

Dia of pipe = 15 cmVelocity of pipe = 2.4 m/sLength of pipe = 1067 mMaximum pressure rise = ?

Velocity of pressure wave in rigid pipe,

Solution

To decide about the type of valve closure,

Case 1: when T = 1 sec.

as; T<2L/C (rapid valve closure)

Solution

Case 2: when T = 5 sec.

as; T>2L/C (slow valve closure)

Problem

An cast iron pipe with 15 cm diameter and 1.5 cm thickness, is conveying water when the outlet is suddenly closed. Calculate the maximum permissible discharge if the pressure rise is not to exceed 1700 KN/m2. take Ev for water as in previous problem and E = 117 x 106 Kpa for cast iron pipe.

Solution

Dia of pipe = 15 cmPipe thickness, t = 1.5 cmMaximum pressure rise = 1700 KN/m2

Ev = 2.06 x 106 KpaE = 117 x 106 KpaMaximum permissible discharge = ?

For velocity of pressure wave in elastic pipe

Solution

For rapid closure,

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