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

Online Pipe Bend Resulting Force Calculator

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

ρ - density of fluid (kg/m³)

d - internal diameter of bend (m)

v- velocity of fluid (m/s)

β - angle of bend (^o)

p - gauge pressure (kPa)

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:

R_x = m v (1 - cosβ) (1)

    = ρ A v² (1 - cosβ) (1b)

    = ρ π (d / 2)² v² (1 - cosβ) (1c)

where

R_x = resulting force in x-direction (N)

m = mass flow (kg/s)

v = flow velocity (m/s)

β = bend angle

ρ = fluid density (kg/m³)

d = internal pipe diameter (m)

π = 3.14...

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

R_y = m v sinβ (2)

    = ρ A v² sinβ (2b)

    = ρ π (d / 2)² v² sinβ  (2c)   

R_y = 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 = (R_x² + R_y²)^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 45^o bend with

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

can be calculated by as 

Resulting force in x-direction:

R_x = 1000 π (0.114 / 2)² 20² (1 - cos45)

    = 1196 (N)

Resulting force in y-direction:

R_y = 1000 π (0.114 / 2)² 20² sin45

    = 2887 (N)

Resulting force on the bend

R = ( 1196² + 2887²)^1/2 

    = 3125 (N)

Note - if β is 90^o 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

R_px = p A (1- cos β) (4)   

    = p π (d / 2)² (1- cos β) (4)

where

R_px = 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

R_py = p π (d / 2)² sinβ (5)

where

R_py = 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:

R_p = (R_px² + R_py²)^1/2 (6)

where

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

Example - Resulting force on a bend due to pressure

The resulting force on a 45^o bend with

• diameter 114 mm
• pressure 100 kPa

can be calculated by as 

Resulting force in x-direction:

R_x = 100 π (0.114 / 2)² (1 - cos45)

    = 299 (N)

Resulting force in y-direction:

R_y = 100 π (0.114 / 2)² sin45

    = 722 (N)

Resulting force on the bend

R = ( 1196² + 2887²)^1/2 

    = 781 (N)

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