WORLD FOR CIVIL

Forces Due To Pipe Bends

The momentum change and the unbalanced internal pressure of the water leads to forces on the pipes

The force diagram in figure is a convenient method for finding the resultant force on a bend. The forces can be resolved into X and Y components to find the magnitude and direction of the resultant force on the pipe.

V₁= velocity before change in size of pipe, ft /s (m/s)

V₂= velocity after change in size of pipe, ft /s (m/s)

p₁= pressure before bend or size change in pipe, lb/ft²
(kPa)

p₂= pressure after bend or size change in pipe, lb/ft²
(kPa)
A₁= area before size change in pipe, ft² (m²)

A₂= area after size change in pipe, ft² (m²)

F_2m= force due to momentum of water in section 2 V₂Qw/g

F_1m= force due to momentum of water in section 1 V₁Qw/g

P₂= pressure of water in section 2 times area of section 2 p₁ A₁

P₁= pressure of water in section 1 times area of section 1 p₁ A₁

w= unit weight of liquid, lb/ft³ (kg/m³)

Q= discharge, ft³/s (m³/s)

If the pressure loss in the bend is neglected and there is no change in magnitude of velocity around the bend,then

R=2A[(wV²/g)+p]cosine of angle between pipes

where R resultant force on bend, lb (N)

p= pressure, lb/ft² (kPa)

w= unit weight of water, 62.4 lb/ft³ (998.4 kg/m³)

V= velocity of flow, ft/s (m/s)

g= acceleration due to gravity, 32.2 ft/s² (9.81 m/s²)

A= area of pipe, ft² (m²)