Water hammer

1.- Input data

Operating pressure and flowrate Pipe section area 3.- Celerity 4.- Velocity change
pop = 13.8 bar A= (pi()/4)*d^2 Initial velocity ptot_SS = pop + hSS Michad
m3/h
c
Q= 636.0 d= 0.2027 m a  vi = 5.47 m/s pop = 13.8 bar hNSS 
2  L  Dv
m2  K d  g  Dt
A= 0.0323 1 
   Final velocity hSS = 70.4 bar
Pipe data  Et s 
 vf = 0.00 m/s ptot_SS = 84.2 bar tc
hNSS h SS 
Material: Carbon Steel Fluid velocity Velocity change Dt
dn = 8 in v= Q/A a : celerity (wave velocity) (m/s) Dv = vf - vi m/s
Dv =
3
sch = 40 - Q= 0.1767 m /s c: speed of sound (m/s) -5.47 m/s Joujovsky
L= 1524.0 m A= 0.0323 m2 d: inside pipe diameter (mm) a  Dv
hSS 
Steel pipe elasticity module v= 5.47 m/s s: minimum wall thickness (mm) 5.- Pressure increment due to water g
Et = 2,059,397 bar K: water bulk modulus (bar) hammer produced by a sudden shutoff.
2 L
s Wave speed in water a= c / (1 + (K/Et) * (d/s) )^(0.5) The pressure increment can be tc 
a
Bulk modulus and density of water c= 1438 m/s calculated with Joukovsky elasticity
K
K= 20,684 bar c K= 2.1E+09 Pa theory, by a Sudden Shutoff "SS"
r= 1,000 kg/m³
r Et = 2.1E+11 Pa
c: speed of sound (m/s) d= 202.74 mm hSS = (- a * Dv ) / g Et = 2,059,397 bar
2.- Auxiliary variables K: water bulk modulus (Pa) s= 8.18 mm a= 1286.9 m/s s
Pipe dimensions r: water density (kg/m³) a= 1287 m/s Dv = -5.47 m/s Bulk modulus and density of water
di = Pipe_Imp_CS_Dint_dn_sch c (K / r )^0.5 h= 718 m K= 20,684 bar
di = 202.74 mm K= 2.1E+09 Pa hSS = 70.4 bar
s= Pipe_Imp_CS_Thickness_dn_sch r= 1000 kg/m³
s= 8.18 mm c= 1438 m/s www.piping-tools.net
Water hammer. Water and slurry hammer

7. Critical time Michaud (Not sudden)

8.- Pressure increment due to water 9. Pressure developed due to valve
Maximum over- pressure or under- 2  L  Dv hammer produced by a Not Sudden shutoff in the time interval Dt > tc
hNSS 
pressure are obtained when the g  Dt Shutoff "NSS" with
shutoff time "Dt", is less or equal to Dt = 5.0 s
Dv 2  L
the critical time "tc", hNSS   For a shutoff time greater than the ptot_NSS = pop + hNSS
g  Dt
2 L critical time, the Michaud relation can pop = 13.8 bar
tc  hNSS 
a  Dv 2  L
 be used. hNSS = 33.4 bar
a g  a  Dt hNSS h SS 
tc ptot_NSS = 47.2 bar
Dt
tc = 2*L/a a  Dv
 h SS hNSS: presure increment in a Non
L= 1,524 m g
a= 1287 m/s Sudden Shutoff
2 L
tc = 2.4 s hNSS  h SS  hSS : Pressure increment in a Sudden
a  Dt Shutoff (Joukovsky)
SS: sudden shutoff 2 L 1 tc : Critical time
hNSS  h SS  
NS: Not sudden shutoff a Dt Dt : Valver closing time Bulk modulus of water
with K= 2.1E+09 Pa
Let valve closing time K= 20,684 bar
2 L Dt =
tc  5.0 s
a Steel elasticity modulus
Pressure ncrement (NSS) Et = 2.10E+06 kp/cm²
1
hNSS  h SS t c  hNSS = hSS *( tc / Dt ) Et = 2.06E+11 Pa
Dt
hSS = 70.4 bar Et = 2.1E+06 bar
t
hNSS  h SS  c tc = 2.4 s
Dt Dt = 5.0 s
hNSS = 33.4 bar