WATER HAMMERMUHAMMAD AKBAR

2005-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.

EFFECTS OF WATER HAMMER

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

DEMAGE CAUSE BY WATER HAMMER

DEMAGE CAUSE 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 te liquid in Kg/m3

for water typical value of Ev = 2.07 x 106

KN/m2

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

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

DEVELOPMENT OF WATER HAMMER

PRESSURE

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. Under steady-state conditions, the flow velocity is v0.

CASE 2

The 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.

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.

CASE 4

A 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.

CASE 5

Upon arrival at the closed gate valve, the velocity changes from -v0 to v = 0. This causes a sudden negative change in pressure of -h.

CASE 6

The 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.

CASE 7

The reservoir is reached in a time t = 3/2Tr, and the pressure resumes the reservoir’s pressure head.

CASE 8

In 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.

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.

PRESSURE VARIATION WITH TIME AT DIFFERENT SECTIONS

1. Figure shows that water hammer pressure Ph as a function of time at various location of the pipe. It is seen that all locations the time period for a complete cycle is 4L/C.

2. The time To = 2L/C, is called as critical time.

AT POINT A

4L/C

2L/C

Ph+

Ph-

AT POINT “A”

Pressure is discontinous and water hammer pressure occur for very short time “T” nearly equal to zero time period for one cycle is 4L/C, so this section of pipe come under pressure either positive or negative for extremely short interval

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

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

vessel water,

Surge tanks

PRACTICAL APPLICATION OF WATER HAMMER

PROBLEMWater 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)

PROBLEMAn 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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