# Horizontal Force in Pipe Bending

In summary, The problem involves water flow through a pipe with a contraction and then into the atmosphere. The given or calculated parameters are Q, A1, A2, u1, u2, p1, p2, θ, ρ, and m. Using the equation Fx = p2A2cosθ-p1A1-m(u2cosθ-u1), the result is -0.011241193N. However, since Fx is negative, it will point in the opposite direction from the way it was drawn on the sketch.

## Homework Statement

Water enters a pipe and goes through a bend with a contraction from 40mm to 25mm then into the atmosphere.
What is the horizontal force required to hold the pipe in place?

## Homework Equations

I have either been given the following or have calculated them using the standard formula, I am confident that they are correct.

Q = 0.01m3s-1
A1 = 1.26 x 10-3m2
A2 = 4.91 x 10-4m2
u1 = 7.94ms-1
u2 = 20.37ms-1
p1 = 31.52Pa
p2 = 207.47Pa
θ = 60°
ρ = 1kgm-3
m = u1A1ρ = 0.0100044

## The Attempt at a Solution

Fx = p2A2cosθ-p1A1-m(u2cosθ-u1)

Using the above equation that I found from a few online sources I get the result:
-0.011241193N

So does this mean I multiply my answer my -1 to make it positive and this is the final result? Or have I gone wrong in my equation?

Any help is appreciated,

You should always draw an sketch of the situation and place a force, Fx, on it. Then do a force balance to determine Fx. If Fx < 0, it will actually point in the opposite direction from the way you drew it.

In your case if you drew the sketch, Fx would be pointing in the direction of the force denoted by P1A1.

## 1. What is horizontal force in pipe bending?

Horizontal force in pipe bending is the force that is applied perpendicular to the direction of the pipe's curvature. It is also known as lateral force and is responsible for causing the pipe to bend or deform horizontally.

## 2. Why is horizontal force important in pipe bending?

Horizontal force is important in pipe bending because it determines the amount of deflection or bending that will occur in the pipe. It also affects the structural integrity of the pipe and can lead to failure if not properly accounted for.

## 3. How is horizontal force calculated in pipe bending?

Horizontal force in pipe bending can be calculated using the formula F = E * I * (d^2y/dx^2), where F is the horizontal force, E is the modulus of elasticity of the pipe material, I is the moment of inertia of the cross section of the pipe, and (d^2y/dx^2) is the second derivative of the deflection curve.

## 4. What factors can affect horizontal force in pipe bending?

There are several factors that can affect horizontal force in pipe bending, including the material properties of the pipe, the shape and size of the pipe, the applied load, and the supports or restraints in place. Temperature changes and external forces such as wind can also impact horizontal force.

## 5. How can horizontal force be minimized in pipe bending?

To minimize horizontal force in pipe bending, it is important to select a pipe material with high elasticity and strength, use proper supports and restraints, and carefully consider the applied load and external factors. Proper design and installation techniques can also help reduce the effects of horizontal force on the pipe.

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