Water Hammer

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Water Hammer

Water hammer ( \(WH\) ) occurs when a valve is suddenly opened or closed. This can creates a repeating pressure wave of the liquid in the pipe that could cause a rupture to the pipe or even damage equipment. As a liquid is traveling through the pipe at a high pressure and the valve is suddenly closed, the flow and pressure come to a sudden stop dropping both to 0. When the valve is closed slower the pressure has a chance to equal out. The resulting sound created is like a hammer, hence water hammer.

Most people are familiar with water hammer in the home when a faucet is shut off or the toilet is flushed, that's the banging or rattling sound you hear in the pipes.

 

" Water Hammer Pressure "

Water Hammer Pressure Increase

Water Hammer Pressure Increase Formula

\(\large{ p_{inc} =   \frac { 0.070 v l  }   { t  } + p_i  }\)                 

Where:

\(\large{ p_{inc} }\) = pressure increase

\(\large{ l }\) = upstream pipe length

\(\large{ p_i }\) = inlet pressure

\(\large{ t }\) = valve closing time

\(\large{ v }\) = flow velocity

Water Hammer Flow Velocity

Water Hammer Flow Velocity Formula

\(\large{ v =   \frac { \left( \; p_{inc} \;-\; p_i  \; \right) t }   { 0.070 l  }  }\)                  

Where:

\(\large{ v }\) = flow velocity

\(\large{ l }\) = upstream pipe length

\(\large{ p_{inc}  }\) = pressure increase

\(\large{ p_i }\) = inlet pressure

\(\large{ t }\) = valve closing time

Water Hammer Upstream Pipe Length

Water Hammer Upstream Pipe Length Formula

\(\large{ l =   \frac { \left( \; p_{inc} \;-\; p_i  \; \right) t }   { 0.070 v  }  }\)                  

Where:

\(\large{ l }\) = upstream pipe length

\(\large{ p_{inc}  }\) = pressure increase

\(\large{ p_i }\) = inlet pressure

\(\large{ t }\) = valve closing time

\(\large{ v }\) = flow velocity

Water Hammer Valve Closing Time

Water Hammer Valve Closing Time Formula

\(\large{ t =   \frac { 0.070 v l  }   {  p_{inc} \;-\; p_i  }   }\)                 

Where:

\(\large{ t }\) = valve closing time

\(\large{ l }\) = upstream pipe length

\(\large{ p_{inc} }\) = pressure increase

\(\large{ p_i }\) = inlet pressure

\(\large{ v }\) = flow velocity

Water Hammer Inlet Pressure

Water Hammer Inlet Pressure Formula

\(\large{ p_i  =  p_{inc}  \;-\; \frac { 0.070 v l  }   { t  }   }\)                 

Where:

\(\large{ p_i }\) = inlet pressure

\(\large{ l }\) = upstream pipe length

\(\large{ p_{inc} }\) = pressure increase

\(\large{ t }\) = valve closing time

\(\large{ v }\) = flow velocity

 

 

" Water Hammer Surge Pressure " 

Water Hammer Maximum Surge Pressure Head

Water Hammer Maximum Surge Pressure Head Formula

\(\large{  H_{sp}  =  \frac { \alpha  \Delta v   }   { g  }   }\)                  

Where:

\(\large{ H_{sp} }\) = maximum surge pressure head in length of pipe

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ \Delta v }\) = fluid velocity change

\(\large{ v }\) = flow velocity

Water Hammer Pressure Wave Velocity

Water Hammer Pressure Wave Velocity Formula

\(\large{  \alpha  =  \frac {  H_{sp}  g  }   { \Delta v  }   }\)                  

Where:

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ H_{sp} }\) = maximum surge pressure head in length of pipe

\(\large{ \Delta v }\) = fluid velocity change

\(\large{ v }\) = flow velocity

Water Hammer Fluid Velocity Change

Water Hammer Fluid Velocity Change Formula

\(\large{  \Delta v  =  \frac {  H_{sp}  g  }   { \alpha  }   }\)                  

Where:

\(\large{ \Delta v }\) = fluid velocity change

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ H_{sp} }\) = maximum surge pressure head in length of pipe

\(\large{ v }\) = flow velocity

Water Hammer Acceleration of Gravity

Water Hammer Acceleration of Gravity Formula

\(\large{ g  =  \frac {  \alpha  \Delta v  }   { H_{sp}  }   }\)                  

Where:

\(\large{ g }\) = acceleration of gravity

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ H_{sp} }\) = maximum surge pressure head in length of pipe

\(\large{ v }\) = flow velocity

\(\large{ \Delta v }\) = fluid velocity change

 

 

" Water Hammer for a Fluid "

Water Hammer Maximum Surge Pressure for a Fluid

Water Hammer Maximum Surge Pressure for a Fluid Formula

\(\large{  p_{spf}  =  \frac { \alpha  \Delta v_f  \gamma  }   { 144 g  }  }\)                         

Where:

\(\large{ p_{spf} }\) = maximum surge pressure for a fluid

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ \Delta v_f }\) = fluid velocity change

\(\large{ \gamma }\)  (Greek symbol gamma) = unit weight of a fluid

Water Hammer Pressure Wave Velocity for a Fluid

Water Hammer Pressure Wave Velocity for a Fluid Formula

\(\large{  \alpha  =  \frac { 144  p_{spf} g  }   { \Delta v_f  }   }\)                  

Where:

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ p_{spf} }\) = maximum surge pressure for a fluid

\(\large{ \Delta v_f }\) = fluid velocity change

\(\large{ \gamma }\)  (Greek symbol gamma) = unit weight of a fluid

Water Hammer Velocity change for a Fluid

Water Hammer Pressure Wave Velocity for a Fluid Formula

\(\large{  \Delta v_f  =  \frac { 144  p_{spf} g  }   { \alpha  \gamma }   }\)                 

Where:

\(\large{ \Delta v_f }\) = fluid velocity change

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ p_{spf} }\) = maximum surge pressure for a fluid

\(\large{ \gamma }\)  (Greek symbol gamma) = unit weight of a fluid

Water Hammer Acceleration of Gravity for a Fluid

Water Hammer Maximum Surge Pressure for a Fluid Formula

\(\large{  g  =  \frac { \alpha  \Delta v_f  \gamma   }   { 144 p_{spf}  }  }\)                         

Where:

\(\large{ g }\) = acceleration of gravity

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ p_{spf} }\) = maximum surge pressure for a fluid

\(\large{ \Delta v_f }\) = fluid velocity change

\(\large{ \gamma }\)  (Greek symbol gamma) = unit weight of a fluid

Water Hammer Unit Weight for a Fluid

Water Hammer Unit Weight for a Fluid Formula

\(\large{  \gamma  =  \frac { 144  p_{spf} g  }   { \alpha  \Delta v_f  }   }\)                  

Where:

\(\large{ \gamma }\)  (Greek symbol gamma) = unit weight of a fluid

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ p_{spf} }\) = maximum surge pressure for a fluid

\(\large{ \Delta v_f }\) = fluid velocity change

 

 

" Water Hammer for Water "

Water Hammer Maximum Surge Pressure for Water

Water Hammer Maximum Surge Pressure for Water Formula

\(\large{  p_{spw}  =  \frac { \alpha  \Delta v_w   }   { 2.31g  }  }\)                         

Where:

\(\large{ p_{spw} }\) = maximum surge pressure for water

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ \Delta v_w }\) = water velocity change

Water Hammer Pressure Wave Velocity for Water

Water Hammer Pressure Wave Velocity for Water Formula

\(\large{  \alpha  =  \frac { 2.31  p_{spw} g  }   { \Delta v  }   }\)                  

Where:

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ p_{spw} }\) = maximum surge pressure for water

\(\large{ \Delta v_w }\) = water velocity change

Water Hammer Velocity change for Water

Water Hammer Pressure Wave Velocity for Water Formula

\(\large{  \Delta v_w  =  \frac { 2.31  p_{spw} g  }   { \alpha  }   }\)                  

Where:

\(\large{ \Delta v_w }\) = water velocity change

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ g }\) = acceleration of gravity

\(\large{ p_{spw} }\) = maximum surge pressure for water

Water Hammer Acceleration of Gravity for Water

Water Hammer Maximum Surge Pressure for Water Formula

\(\large{  g  =  \frac { \alpha  \Delta v_w   }   { 2.31 p_{spw}  }  }\)                         

Where:

\(\large{ g }\) = acceleration of gravity

\(\large{ \alpha }\)  (Greek symbol alpha) = pressure wave velocity

\(\large{ p_{spw} }\) = maximum surge pressure for water

\(\large{ \Delta v_w }\) = water velocity change

 

Tags: Equations for Velocity Equations for Pressure Equations for Valves Equations for Gas Equations for Water Equations for Pipe