Horizontal Force in Pipe Bending

[adam640]

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

F_x = 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,

Adam

 

[LawrenceC]

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.