# 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 Increase

### Water Hammer Pressure Increase Formula

$$p_{inc} = \frac { 0.070 v l } { t } + p_i$$          $$pressure \; increase \;=\; \frac { 0.070 \;\;x\;\; flow \; velocity \;\;x\;\; upstream \; pipe \; length } { valve \; closing \; time } \;+\; inlet \; pressure$$

Where:

$$p_{inc}$$ = pressure increase

$$l$$ = upstream pipe length

$$p_i$$ = inlet pressure

$$t$$ = valve closing time

$$v$$ = flow velocity

## Water Hammer Flow Velocity

### Water Hammer Flow Velocity Formula

$$v = \frac { \left( \; p_{inc} \;-\; p_i \; \right) t } { 0.070 l }$$          $$flow \; velocity \;=\; \frac { \left( \; pressure \; increase \;-\; inlet \; pressure \; \right) \; valve \; closing \; time } { 0.070 \;\;x\;\; upstream \; pipe \; length }$$

Where:

$$v$$ = flow velocity

$$l$$ = upstream pipe length

$$p_{inc}$$ = pressure increase

$$p_i$$ = inlet pressure

$$t$$ = valve closing time

## Water Hammer Upstream Pipe Length

### Water Hammer Upstream Pipe Length Formula

$$l = \frac { \left( \; p_{inc} \;-\; p_i \; \right) t } { 0.070 v }$$          $$upstream \; pipe \; length \;=\; \frac { \left( \; pressure \; increase \;-\; inlet \; pressure \; \right) \; valve \; closing \; time } { 0.070 \;\;x\;\; flow \; velocity }$$

Where:

$$l$$ = upstream pipe length

$$v$$ = flow velocity

$$p_{inc}$$ = pressure increase

$$p_i$$ = inlet pressure

$$t$$ = valve closing time

## Water Hammer Valve Closing Time

### Water Hammer Valve Closing Time Formula

$$t = \frac { 0.070 v l } { p_{inc} \;-\; p_i }$$          $$valve \; close \; time \;=\; \frac { 0.070 \;\;x\;\; flow \; velocity \;\;x\;\; upstream \; pipe \; length } { pressure \; increase \;-\; inlet \; pressure }$$

Where:

$$t$$ = valve closing time

$$l$$ = upstream pipe length

$$v$$ = flow velocity

$$p_{inc}$$ = pressure increase

$$p_i$$ = inlet pressure

## Water Hammer Inlet Pressure

### Water Hammer Inlet Pressure Formula

$$p_i = p_{inc} \;-\; \frac { 0.070 v l } { t }$$          $$inlet \; pressure \;=\; pressure \; increase \;-\; \frac { 0.070 \;\;x\;\; flow \; velocity \;\;x\;\; upstream \; pipe \; length } { valve \; closing \; time }$$

Where:

$$p_i$$ = inlet pressure

$$t$$ = valve closing time

$$l$$ = upstream pipe length

$$v$$ = flow velocity

$$p_{inc}$$ = pressure increase

## Water Hammer Maximum Surge Pressure Head

### Water Hammer Maximum Surge Pressure Head Formula

$$H_{sp} = \frac { \alpha \Delta v } { g }$$          $$maximum \; surge \; pressure \; head \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; fluid \; velocity \; change } { acceleration \; of \; gravity }$$

Where:

$$H_{sp}$$ = maximum surge pressure head in length of pipe

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v$$ = fluid velocity change

$$v$$ = flow velocity

$$g$$ = acceleration of gravity

## Water Hammer Pressure Wave Velocity

### Water Hammer Pressure Wave Velocity Formula

$$\alpha = \frac { H_{sp} g } { \Delta v }$$          $$pressure \; wave \; velocity \;=\; \frac { maximum \; surge \; pressure \; head \;\;x\;\; acceleration \; of \; gravity } { fluid \; velocity \; change }$$

Where:

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$H_{sp}$$ = maximum surge pressure head in length of pipe

$$\Delta v$$ = fluid velocity change

$$v$$ = flow velocity

$$g$$ = acceleration of gravity

## Water Hammer Fluid Velocity Change

### Water Hammer Fluid Velocity Change Formula

$$\Delta v = \frac { H_{sp} g } { \alpha }$$          $$fluid \; velocity \; change \;=\; \frac { maximum \; surge \; pressure \; head \;\;x\;\; acceleration \; of \; gravity } { pressure \; wave \; velocity }$$

Where:

$$\Delta v$$ = fluid velocity change

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$H_{sp}$$ = maximum surge pressure head in length of pipe

$$v$$ = flow velocity

$$g$$ = acceleration of gravity

## Water Hammer Acceleration of Gravity

### Water Hammer Acceleration of Gravity Formula

$$g = \frac { \alpha \Delta v } { H_{sp} }$$          $$acceleration \; of \; gravity \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; fluid \; velocity \; change } { maximum \;surge \; pressure \; head }$$

Where:

$$g$$ = acceleration of gravity

$$\Delta v$$ = fluid velocity change

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$H_{sp}$$ = maximum surge pressure head in length of pipe

$$v$$ = flow velocity

## Water Hammer Maximum Surge Pressure for a Fluid

### Water Hammer Maximum Surge Pressure for a Fluid Formula

$$p_{spf} = \frac { \alpha \Delta v_f \gamma } { 144 g }$$          $$maximum \; surge \; pressure \; for \; a \; fluid \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; fluid \; velocity \; change \;\;x\;\; unit \; weight \; of \; a \; fluid } { 144 \;\;x\;\; acceleration \; of \; gravity }$$

Where:

$$p_{spf}$$ = maximum surge pressure for a fluid

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_f$$ = fluid velocity change

$$g$$ = acceleration of gravity

$$\gamma$$ (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

$$\alpha = \frac { 144 p_{spf} g } { \Delta v_f }$$          $$pressure \; wave \; velocity \;=\; \frac { 144 \;\;x\;\; maximum \; surge \; pressure \; for \; a \; fluid \;\;x\;\; acceleration \; of \; gravity } { fluid \; velocity \; change }$$

Where:

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_f$$ = fluid velocity change

$$p_{spf}$$ = maximum surge pressure for a fluid

$$g$$ = acceleration of gravity

$$\gamma$$ (Greek symbol gamma) = unit weight of a fluid

## Water Hammer Velocity change for a Fluid

### Water Hammer Pressure Wave Velocity for a Fluid Formula

$$\Delta v_f = \frac { 144 p_{spf} g } { \alpha \gamma }$$          $$fluid \; velocity \; change \;=\; \frac { 144 \;\;x\;\; maximum \; surge \; pressure \; for \; a \; fluid \;\;x\;\; acceleration \; of \; gravity } { pressure \; wave \; velocity \;\;x\;\; unit \; weight \; of \; a \; fluid }$$

Where:

$$\Delta v_f$$ = fluid velocity change

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$p_{spf}$$ = maximum surge pressure for a fluid

$$g$$ = acceleration of gravity

$$\gamma$$ (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

$$g = \frac { \alpha \Delta v_f \gamma } { 144 p_{spf} }$$          $$acceleration \; of \; gravity \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; fluid \; velocity \; change \;\;x\;\; unit \; weight \; of \; a \; fluid } { 144 \;\;x\;\; maximum \; surge \; pressure \; for \; a \; fluid }$$

Where:

$$g$$ = acceleration of gravity

$$p_{spf}$$ = maximum surge pressure for a fluid

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_f$$ = fluid velocity change

$$\gamma$$ (Greek symbol gamma) = unit weight of a fluid

## Water Hammer Unit Weight for a Fluid

### Water Hammer Unit Weight for a Fluid Formula

$$\gamma = \frac { 144 p_{spf} g } { \alpha \Delta v_f }$$          $$unit \; weight \; of \; a \; fluid \;=\; \frac { 144 \;\;x\;\; maximum \; surge \; pressure \; for \; a \; fluid \;\;x\;\; acceleration \; of \; gravity } { pressure \; wave \; velocity \;\;x\;\; fluid \; velocity \; change }$$

Where:

$$\gamma$$ (Greek symbol gamma) = unit weight of a fluid

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_f$$ = fluid velocity change

$$p_{spf}$$ = maximum surge pressure for a fluid

$$g$$ = acceleration of gravity

## Water Hammer Maximum Surge Pressure for Water

### Water Hammer Maximum Surge Pressure for Water Formula

$$p_{spw} = \frac { \alpha \Delta v_w } { 2.31g }$$          $$maximum \; surge \; pressure \; for \; water \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; water \; velocity \; change } { 2.31 \;\;x\;\; acceleration \; of \; gravity }$$

Where:

$$p_{spw}$$ = maximum surge pressure for water

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_w$$ = water velocity change

$$g$$ = acceleration of gravity

## Water Hammer Pressure Wave Velocity for Water

### Water Hammer Pressure Wave Velocity for Water Formula

$$\alpha = \frac { 2.31 p_{spw} g } { \Delta v }$$          $$pressure \; wave \; velocity \;=\; \frac { 2.31 \;\;x\;\; maximum \; surge \; pressure \; for \; water \;\;x\;\; acceleration \; of \; gravity } { water \; velocity \; change }$$

Where:

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_w$$ = water velocity change

$$p_{spw}$$ = maximum surge pressure for water

$$g$$ = acceleration of gravity

## Water Hammer Velocity change for Water

### Water Hammer Pressure Wave Velocity for Water Formula

$$\Delta v_w = \frac { 2.31 p_{spw} g } { \alpha }$$          $$water \; velocity \; change \;=\; \frac { 2.31 \;\;x\;\; maximum \; surge \; pressure \; for \; water \;\;x\;\; acceleration \; of \; gravity } { pressure \; wave \; velocity }$$

Where:

$$\Delta v_w$$ = water velocity change

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$p_{spw}$$ = maximum surge pressure for water

$$g$$ = acceleration of gravity

## Water Hammer Acceleration of Gravity for Water

### Water Hammer Maximum Surge Pressure for Water Formula

$$g = \frac { \alpha \Delta v_w } { 2.31 p_{spw} }$$          $$acceleration \; of \; gravity \;=\; \frac { pressure \; wave \; velocity \;\;x\;\; water \; velocity \; change } { 2.31 \;\;x\;\; maximum \; surge \; pressure \; for \; water }$$

Where:

$$g$$ = acceleration of gravity

$$p_{spw}$$ = maximum surge pressure for water

$$\alpha$$ (Greek symbol alpha) = pressure wave velocity

$$\Delta v_w$$ = water velocity change