Maximum Pressure Surge Generated by Instantaneous Valve Shutoff - Maple Programming Help

Home : Support : Online Help : Applications and Example Worksheets : Science and Engineering : applications/MaxPressureSurge

Maximum Pressure Surge Generated by Instantaneous Valve Shutoff

Introduction

This application calculates the excess pressure generated by water hammer when a valve at the end of a pipeline instantaneously closes

 > $\mathrm{restart}:\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Standard}\right]\right):$

Parameters

Fluid density:

 >

Fluid velocity change:

 >

Bulk modulus of fluid:

 >

Young's modulus of pipe:

 >

Pipe wall thickness:

 > 

Intermediate Calculations

Effective bulk modulus:

 >

Speed of sound:

 > $\mathrm{c}≔\mathrm{PipeID}\to {\left(\frac{\mathrm{Ke}\left(\mathrm{PipeID}\right)}{\mathrm{\rho }}\right)}^{\frac{1}{2}}:$

Maximum pressure surge:

 > $\mathrm{ΔP}≔\mathrm{PipeID}\to \mathrm{ρ}\cdot \mathrm{c}\left(\mathrm{PipeID}\right)\cdot \mathrm{Δv}:$

Results

 > $\mathrm{plot}\left(\mathrm{ΔP}\left(\mathrm{PipeID}\right),\mathrm{PipeID}=0.1..0.2,\mathrm{labels}=\left["Pipe ID \left(m\right)","Excess Pressure \left(Pa\right)"\right],\mathrm{labeldirections}=\left[\mathrm{horizontal},\mathrm{vertical}\right],\mathrm{labelfont}=\left[\mathrm{Calibri}\right],\mathrm{title}="Magnitude of Pressure Surge Due to Valve Closure",\mathrm{titlefont}=\left[\mathrm{Calibri},14\right],\mathrm{size}=\left[600,400\right],\mathrm{axesfont}=\left[\mathrm{Calibri}\right],\mathrm{axis}\left[1\right]=\left[\mathrm{gridlines}=\left[\mathrm{linestyle}=\mathrm{dot}\right]\right],\mathrm{axis}\left[2\right]=\left[\mathrm{gridlines}=\left[\mathrm{linestyle}=\mathrm{dot}\right]\right],\mathrm{color}=\mathrm{ColorTools}:-\mathrm{Color}\left("RGB",\left[0/255,79/255,121/255\right]\right)\right)$
 >