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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
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Online Pipe Bend Resulting Force Calculator
The calculator below can used to calculate resulting force in piping bends: -------------------------------------------------
Top of FormMetricρ - 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)Bottom of Form | -------------------------------------------------
Top of FormImperial 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)Bottom of Form |
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 - cos45) = 1196 (N)
Resulting force in y-direction:
Ry = (1000 kg/m3) π ((0.114 m) / 2)2 (20 m/s)2 sin45 = 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 - cos45) = 299 (N)
Resulting force in y-direction:
Ry = (100 kPa) π ((0.114 m) / 2)2 sin45 = 722 (N)
Resulting force on the bend
R = ((299 N)2 + (722 N)2)1/2 = 781 (N)

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