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The forces created in Pipe bends by a combination of static, dynamic,and frictional forces.

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Introduction

Fluids flowing round bends in pipes suffer from an increase in turbulence and a consequential increase the head lost in the pipe. They also produce forces on the bend which are examined in this section.

Forces on Pipe Bends

The Total or Resultant Thrust on a Pipe Elbow will be made up of :-

The Static Pressure Force.

A Dynamic Force due to the change in direction of the fluid flow. This is the product of the mass of fluid passing through the bend per second times the change in velocity.

The frictional forces on the Pipe

The weight of the elbow and the fluid contained in it.

In general these last two are small and can be neglected.

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Considering the $90^0$ elbow shown in the diagram.

Force in Direction X:-

$R_X=p_1a_1+\frac{wa_1{v_{1}}^{2}}{g}$

(1)

Force in Direction Y:-

$R_Y=p_2a_2+\frac{wa_2{v_{2}}^{2}}{g}$

(2)

Resultant Force R

$R=\sqrt{{R_{X}}^{2}+{R_{Y}}^{2}}$

(3)

R has a direction measured from the X axis of :-

$\theta=\tan^{-1}\frac{R_Y}{R_X}$

(4)

The solution to the following example can be seen by pressing the red button.

Example 1

A pipe AB of 1 ft. diameter carries water at 12 ft./sec. down to a Power-house. At A and B there are frictionless expansion joints and the pipe which weighs 40 lb./ft.run, is mounted on frictionless rollers, except where it is tied in the concrete block C

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At A the head is 120 ft. and f for the pipe is 0.0075

Determine the horizontal and vertical components of the force on the block c due to the pipe line. (B.Sc. Part 2)

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