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Unbalanced Thrust Force due to Internal Pressure

 

Unbalanced Thrust Force due to Internal Pressure (Unrestrained Straight Pipe) formula

  • This force is the internal pressure acting on the area at the end of a pipe or at an expansion joint, and it is reacted by the pipe material or external anchor.

\(  F  \;=\;  p \cdot  A_c  \)     (Unrestrained Straight Pipe)

\(  p  \;=\;  \dfrac{ F }{  A_c  }\)

\(  A_c  \;=\;  \dfrac{ F }{  p }\)
Symbol English Metric
\( F \)  = Internal Thrust Force \(lbf\) \(N\)
\( p \) = Internal Pressure \(lbf \;/\; in^2\) \(Pa\)
\( A_c \) = Area Cross-section of Pipe \(in^2\) \(mm^2\)

Unbalanced thrust force due to internal pressure, abbreviated as \(F\) or \(T\), is the net axial force that acts on a component, such as a pipe, valves, fittings, or expansion joint, when the internal fluid pressure does not act equally in all opposing directions.  In a straight, uniform pipe the pressure forces on opposite cross-sections balance each other, producing no net thrust.  However, when there is a change in geometry, flow direction, or cross-sectional area, the pressure forces become unequal.  This imbalance results in a thrust force that tends to push or pull the component along the direction of flow.  The magnitude of the unbalanced thrust force depends on the internal pressure and the effective area over which the pressure acts, and it must be resisted by anchors, supports, or restraints to prevent excessive movement, structural damage, or failure of the piping system.

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Unbalanced Thrust Force due to Internal Pressure (Pipe Bend) formula

  • The thrust force is the resultant force created by the pressure acting on the internal surfaces of the bend, like elbows.

\(  F  \;=\; 2 \cdot  p \cdot  A_c \cdot sin\left( \dfrac{ \theta }{ 2 } \right) \)     (Pipe Bend)  

\(  p  \;=\;   \dfrac{  F  }{  2 \cdot  A_c \cdot sin\left( \dfrac{ \theta }{ 2 } \right)  } \)

\(  A_c  \;=\;  \dfrac{  F  }{  2 \cdot  p \cdot sin\left( \dfrac{ \theta }{ 2 } \right)  } \)
Symbol English Metric
\( F \)  = Resultant Thrust Force \(lbf\) \(N\)
\( p \) = Internal Pressure \(lbf \;/\; in^2\) \(Pa\)
\( A_c \) = Area Cross-section of Pipe \(in^2\) \(mm^2\)
\( \theta \) = Pipe Bend Angle \(deg\) \(rad\)

 

 

 

Unbalanced Thrust Force due to Internal Pressure (Reducers) formula

  • The unbalanced force occurs due to the difference in area between the two ends.

\(  F  \;=\;   p \cdot  \left(  A_l  - A_s \right)  \)     (Reducers)

\(  p  \;=\;  \dfrac{  F  }{  A_l  - A_s }  \)

\(  A_l  \;=\;  \dfrac{  F  }{  p } + A_s  \)

\(  A_s  \;=\;  A_l - \dfrac{  F  }{  p }  \)
Symbol English Metric
\( F \)  = InternalThrust Force \(lbf\) \(N\)
\( p \) = Internal Pressure \(lbf \;/\; in^2\) \(Pa\)
\( A_l \) = Area Cross-section of Large End \(in\) \(mm\)
\( A_s \) = Area Cross-section of Small End \(in\) \(mm\)