Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# Piping Elbows - Thrust Block Forces

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

Sponsored Links

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

The resultant force - or required support force - on 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

With no flow and no pressure there is no force.

### 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)

#### Imperial Units

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

v - velocity of fluid (ft/s)

β - turning angle of bend (o)

p - gauge pressure (psi)

### 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

Sponsored Links

## 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

Sponsored Links

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

## Unit Converters

Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

4 15

This website use cookies. By continuing to browse you are agreeing to our use of cookies! Learn more