Piping Elbows  Thrust Block Forces
Thrust block forces on pipe bends anchors due to liquid velocities and internal pressures  online resulting force calculator.
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:
Resulting force due to Mass flow and Flow Velocity
The resulting force in xdirection 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 xdirection (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 ydirection 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 ydirection 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
 internal diameter 102 mm = 0.102 m
 water with density 1000 kg/m^{3}
 flow velocity 20 m/s
can be calculated by as
Resulting force in xdirection:
R_{x} = (1000 kg/m^{3}) π ((0.102 m) / 2)^{2} (20 m/s)^{2} (1  cos(45))
= 957 N
Resulting force in ydirection:
R_{y} = (1000 kg/m^{3}) 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 90^{o }the resulting forces in x and ydirections 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 ydirections.
The resulting force in xdirection 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 xdirection (N)
p = gauge pressure inside pipe (Pa, N/m^{2})
The resulting force in ydirection can be expressed as
R_{py} = p π (d / 2)^{2} sinβ (5)
where
R_{py} = resulting force due to pressure in ydirection (N)
The resulting force on the bend due to force in x and ydirection 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
 internal diameter 102 mm = 0.102 m
 pressure 100 kPa
can be calculated by as
Resulting force in xdirection:
R_{x} = (100 10^{3} Pa) π ((0.102 m) / 2)^{2} (1  cos(45))
= 239 N
Resulting force in ydirection:
R_{y} = (100 10^{3} 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
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