Pipe Bends and Thrust Block Forces

Pipe bends and thrust blocks forces on anchors due to fluid velocity and internal pressure - online resulting force calculator

pipe bend thrust forces

Online Pipe Bend Resulting Force Calculator

The calculator below can used to calculate resulting force in piping bends:

Metric Units

ρ - density of fluid (kg/m3)

d - int. diam. pipe or bend (m)

v - velocity of fluid (m/s)

β - turning angle of bend (o)

p - gauge pressure (kPa)

Imperial Units

 SG - specific gravity of fluid 

d - int. diam. pipe or bend (inches)

v - velocity of fluid (ft/s)

β - turning angle of bend (o)

p - gauge pressure (psi)

The resulting force on a thrust block or anchor depends on the fluid mass flow and flow velocity and the pressure in the bend.

Resulting force due to Mass flow and Flow Velocity

The resulting force in x-direction due to mass flow and flow velocity can be expressed as:

Rx = m v (1 - cosβ)         (1)

    = ρ A v2 (1 - cosβ)         (1b)

    = ρ π (d / 2)2 v2 (1 - cosβ)         (1c)

where

Rx = resulting force in x-direction (N)

m = mass flow (kg/s)

v = flow velocity (m/s)

β = turning bend angle (degrees)

ρ = fluid density (kg/m3)

d = internal pipe or bend diameter (m)

π = 3.14...

The resulting force in y-direction due to mass flow and flow velocity can be expressed as:

Ry = m v sinβ         (2)

    = ρ A v2 sinβ         (2b)

    = ρ π (d / 2)2 v2 sinβ          (2c)   

Ry = resulting force in y direction (N)

The resulting force on the bend due to force in x- and y-direction can be expressed as:

R = (Rx2 + Ry2)1/2         (3)

where

R = resulting force on the bend (N)

Example - Resulting force on a bend due to mass flow and flow velocity

The resulting force on a 45o bend with

  • diameter 114 mm = 0.114 m
  • water with density 1000 kg/m3
  • flow velocity 20 m/s

can be calculated by as 

Resulting force in x-direction:

Rx = (1000 kg/m3) π ((0.114 m) / 2)2 (20 m/s)2 (1 - cos(45))

    = 1196 (N)

Resulting force in y-direction:

Ry = (1000 kg/m3) π ((0.114 m) / 2)2 (20 m/s)2 sin(45)

    = 2887 (N)

Resulting force on the bend

R = (1196 (N)2 + 2887 (N)2)1/2 

    = 3125 (N)

Note - if β is 90o the resulting forces in x- and y-directions are the same.

Resulting force due to Static Pressure

The pressure and the end surfaces of the bend creates resulting forces in x- and y-directions.

The resulting force in x-direction can be expressed as

Rpx = p A (1- cos β)         (4)   

    = p π (d / 2)2 (1- cos β)         (4b)

where

Rpx = resulting force due to pressure in x-direction (N)

p = gauge pressure inside pipe (Pa, N/m2)

The resulting force in y-direction can be expressed as

Rpy = p π (d / 2)2 sinβ         (5)

where

Rpy = resulting force due to pressure in y-direction (N)

The resulting force on the bend due to force in x- and y-direction can be expressed as:

Rp = (Rpx2 + Rpy2)1/2         (6)

where

Rp = resulting force on the bend due to static pressure (N)

Example - Resulting force on a bend due to pressure

The resulting force on a 45o bend with

  • diameter 114 mm = 0.114 m
  • pressure 100 kPa

can be calculated by as 

Resulting force in x-direction:

Rx = (100 kPa) π ((0.114 m) / 2)2 (1 - cos(45))

    = 299 (N)

Resulting force in y-direction:

Ry = (100 kPa) π (0.114 (m) / 2)2 sin(45)

    = 722 (N)

Resulting force on the bend

R = (299 (N)2 + 722 (N)2)1/2 

    = 781 (N)

Related Topics

  • Pressure Ratings - Pressure ratings of pipes and tubes and their fittings - carbon steel , stainless steel, plastic, copper and more
  • Design Strategies - Piping systems and design strategies - documentation, P&ID, flow diagrams - capacities and limits

Related Documents

Key Words

  • en: pipe bend force fluid velocity pressure
  • es: tubo de fuerza de doblado de la velocidad del fluido de presiĆ³n
  • de: Rohrbiegekraft Fluidgeschwindigkeit Druck

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