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Piping Elbows - Thrust Block Forces

Thrust block forces on pipe bends anchor due to liquid velocity and internal pressure - online resulting force calculator

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In a piping structure without adequately support fluid flow velocities and internal pressures may create intolerable forces and tensions. 

Online Pipe Bend Resulting Force Calculator

The calculator below can used to calculate the resulting force in a piping bend:

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)


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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)


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The required support force for a thrust block - or an anchor - for a bend depends on

  • the fluid mass flow, or flow velocity
  • the change of flow direction
  • the internal pressure 

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

  • internal diameter 102 mm = 0.102 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 ((0.102 m) / 2)2 (20 m/s)2 (1 - cos(45))

    = 957 N

Resulting force in y-direction:

Ry = (1000 kg/m3) π ((0.102 m) / 2)2 (20 m/s)2 sin(45)

    = 2311 N

Resulting force on the bend

R = (957 N)2 + (2311 N)2)1/2 

    = 2501 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 "acting" on 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

  • internal diameter 102 mm = 0.102 m
  • pressure 100 kPa

can be calculated by as 

Resulting force in x-direction:

Rx = (100 103 Pa) π ((0.102 m) / 2)2 (1 - cos(45))

    = 239 N

Resulting force in y-direction:

Ry = (100 103 Pa) π ((0.102 m) / 2)2 sin(45)

    = 578 N

Resulting force on the bend

R = ((239 N)2 + (577 N)2)1/2 

    = 625 N

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