# 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:

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:

R_{x}= m v (1 - cosβ) (1)

= ρ A v^{2}(1 - cosβ) (1b)

= ρ π (d / 2)^{2}v^{2}(1 - cosβ) (1c)

where

R_{x}= 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/m^{3})

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:

R_{y}= m v sinβ (2)

= ρ A v^{2}sinβ (2b)

= ρ π (d / 2)^{2}v^{2}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_{x}^{2}+ R_{y}^{2})^{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 = 0.114 m* - water with density
*1000 kg/m*^{3} - flow velocity
*20 m/s*

can be calculated by as

Resulting force in x-direction:

R_{x}= (1000 kg/m^{3}) π ((0.114 m) / 2)^{2}(20 m/s)^{2}(1 - cos(45))

= 1196 (N)

Resulting force in y-direction:

R_{y}= (1000 kg/m^{3}) 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 *90*^{o }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

R_{px}= p A (1- cos β) (4)

= p π (d / 2)^{2}(1- cos β) (4b)

where

R_{px}= resulting force due to pressure in x-direction (N)

p = gauge pressure inside pipe (Pa, N/m^{2})

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_{px}^{2}+ R_{py}^{2})^{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 = 0.114 m* - pressure
*100 kPa*

can be calculated by as

Resulting force in x-direction:

R_{x}= (100 kPa) π ((0.114 m) / 2)^{2}(1 - cos(45))

= 299 (N)

Resulting force in y-direction:

R_{y}= (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)

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