BIZOMAT MAKEOS · Hydraulics
Pipe Bend Thrust Check (Pressure and Momentum Force, Resultant, Thrust Block Bearing)
What force does the water push on this pipe bend from its pressure and flow, and is the thrust block big enough for the ground to carry it?
Thrust on an unrestrained pipe bend: the flow velocity in the pipe (as the pipe friction tool), the pressure force and the momentum force of the flow, the resultant thrust bisecting the bend angle, and the bearing pressure of the thrust block on the ground with the block area needed, against the ground’s allowable bearing pressure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Flow | L/min | Flow through the pipe. |
| Pipe inside diameter | mm | Inside diameter of the pipe. |
| Pressure (test pressure for the worst case) | bar | Internal pressure; use the test pressure, which is usually the worst case. |
| Bend angle (change of direction) | ° | Angle through which the pipe changes direction (90 for an elbow). |
| Liquid density | kg/m³ | Density of the liquid. |
| Thrust block | ||
| Block bearing area against the ground | m² | Area of the block face bearing on undisturbed ground. |
| Allowable ground bearing pressure | kPa | Allowable horizontal bearing pressure of the ground (from a site investigation; soft clays are low). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Flow
- What it is
- The volume of liquid passing through the bend in each minute, used to find the flow velocity and the momentum force on the bend.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 100000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The momentum force rises with the square of the flow, but it is usually a small part of the thrust.
- Get it right
- Enter litres per minute: multiply litres per second by 60, or cubic metres per hour by 1000 ÷ 60.
What this means: Pipe inside diameter
- What it is
- The bore of the pipe at the bend, which sets the area the internal pressure acts on and the flow velocity.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The pressure force rises with the square of the diameter.
- Get it right
- Use the inside diameter, not the nominal size or outside diameter; wall thickness and lining change it.
What this means: Pressure (test pressure for the worst case)
- What it is
- The internal pressure in the pipe at the bend; the field-test pressure is normally the highest the bend and its thrust block will see.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The pressure part of the thrust rises in proportion to it.
- Get it right
- Use gauge pressure in bar (1 bar = 100 kPa), and allow for surge pressure if it can exceed the test pressure.
What this means: Bend angle (change of direction)
- What it is
- How far the pipe turns at the bend: the change of direction between the incoming and outgoing pipe, so a right-angle elbow is the full quarter turn.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The thrust rises with the sine of half this angle, so sharper bends need larger blocks.
- Get it right
- Enter the deflection angle, not the included angle between the two pipe legs; a straight pipe has no deflection.
What this means: Liquid density
- What it is
- The mass per cubic metre of the liquid in the pipe, used for the momentum force of the flow.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the momentum force in proportion; the pressure force does not change.
- Get it right
- Take it from the fluid data at the working temperature; it affects only the small momentum part of the thrust.
Thrust block
What this means: Block bearing area against the ground
- What it is
- The area of the thrust block face that bears against the ground behind the bend, facing the direction of the resultant thrust.
- Units and format
- Enter a number in m²: square metres. The form accepts 0.000001 m² to 10000 m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bearing pressure on the ground falls in proportion as this area grows.
- Get it right
- Count only the face poured against undisturbed ground, measured square to the thrust, not the plan area of the block.
What this means: Allowable ground bearing pressure
- What it is
- The horizontal bearing pressure the ground behind the block can safely take, which the block bearing pressure is checked against.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0.000001 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the block area needed; the thrust does not change.
- Get it right
- Get it from a geotechnical investigation or the responsible engineer; it is in kPa, so 1 MPa is 1000 kPa.
Method and formulas
- Velocity v = Q ÷ A (as the pipe friction tool).
- Thrust = 2 (p A + ρ Q v) sin (θ ÷ 2), acting along the bisector of the bend, outwards.
- Bearing pressure = thrust ÷ block area; area needed = thrust ÷ allowable pressure.
- Example: 25.191 kN of thrust; the block bears at 25.191 kPa (needs 0.33588 m²).
Limitations
- Horizontal bend; vertical bends add or subtract the weight of the pipe, water and block.
- Static pressure dominates at normal velocities; water hammer surges raise the pressure.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a thrust block for a buried water main bend
- Check an anchor at a pump discharge bend
- Find the force on a bend during a pressure test
Who it is for
- Civil and water engineers
- Pipe fitters
- Plant engineers
What you get
- Velocity, pressure and momentum forces
- Resultant thrust
- Block bearing pressure and area needed
Interpreting the result
- At normal pipe velocities the momentum part is only about one per cent of the thrust: the test pressure is what matters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
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