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Momentum and pressure question (fluid mechanics)

Heres the question and the solution:



If its a bit unclear, heres the question typed out:

Calculate the magnitude and direction of the force exerted by the pipe bend shown, if the diameter is 600m, the discharge is 0.3m^3/s and the pressure head at both ends is 30m.



What I don't understand, is how do you know which direction to assume for the reaction forces and pressure forces in your calculation?

For example, for the bit I've circled in red, why is the pressure force (Ap) negative, but for the equation circle in blue, its positive?

Also, the way the reaction force has been draw, it shows the x-component of the force going inwards, which seems bizarre to me, I would've thought reaction should be going out (i,e, facing left instead of right)
I'd like to add my two cents' worth, as no one has replied yet.

The negative signs for the values of F_x and F_{R_x} show that the resulting forces *do* go inwards as you said. I assume that the directions were chosen just because they are the "standard" x-y directions.

I'm not sure about the red and blue bits though - hopefully someone else will see this and help.
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Red Richie
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Original post by firegalley246
I'd like to add my two cents' worth, as no one has replied yet.

The negative signs for the values of F_x and F_{R_x} show that the resulting forces *do* go inwards as you said. I assume that the directions were chosen just because they are the "standard" x-y directions.

I'm not sure about the red and blue bits though - hopefully someone else will see this and help.


Thanks, I can see how F_{R_x} is shown to be negative, and hence at the opposite to the initial assumed direction of it going right. I do understand that they've just randomly assumed a direction for F_{R_x} and F_{R_y} in the blue and red circled equations, the logic being that the +ve/-ve you get at the end for the calculated number would tell you whether your initial assumption was correct.

My main confusion, is how they know the directions for the pressure force (Ap) in both of those equations. Because clearly they haven't just randomly assumed a direction for it, otherwise it would've drastically alter the direction of F_{R_x} and F_{R_y} which we're trying to calculate.

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