WATER HAMMERWATER HAMMER

WATER HAMMERWATER HAMMER

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.

VELOCITY OF PRESSURE WAVEVELOCITY 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 PascalΡ = mass density of te liquid in Kg/m3

for water typical value of Ev = 2.07 x 106 KN/m2

VELOCITY OF PRESSURE WAVEVELOCITY 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 PressureEquation 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 PressureEquation 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 PressureEquation for Water Hammer Pressure

DEVELOPMENT OF DEVELOPMENT OF WATER HAMMER WATER HAMMER

PRESSUREPRESSURE

INSTANTANEOUS VALVE CLOSUREINSTANTANEOUS 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.

Various stages of Water Hammer Various stages of Water Hammer Pressure WavePressure Wave

Pressure variation with time at Pressure variation with time at different sectionsdifferent 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.

RAPID VALVE CLOSURERAPID 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 CLOSURESLOW 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 THICKNESSDESIGN 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 HammerMethod for controlling Water Hammer

1.Slow valve closure2.Pressure relief valve3.Surge tank

Practical Application of Practical Application of Water HammerWater Hammer

ProblemProblemWater 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 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 Solution To decide about the type of valve closure,

Case 1: when T = 1 sec.

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

Solution Solution Case 2: when T = 5 sec.

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

ProblemProblemAn 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 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 Solution

For rapid closure,

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