What is the Force Exerted on Supports Holding a 90 Degree Reducing Bend Pipe?

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Homework Statement


A 90 degree reducing bend has an inlet diameter of 4 in. and an outlet diameter of 2 in. If water enters the bend at a pressure of 40 psig and a flow of 500 gpm, calculate the force (net magnitude and direction) exerted on the supports that hold the bend in lace. The loss coefficient (number of velocity heads lost due to fluid frictional drag) is 0.75 based on the highest velocity in the bend.


Homework Equations





The Attempt at a Solution



For this problem, I am having troubles finding the pressure at the outlet, as well as the force of gravity in my first momentum balance in the y-direction since I don't know the volume of the pipe. Also, I'm not sure which direction the drag force should go, I've seen it in the lecture notes as being positive in a situation where water was flowing up a pipe, which seems odd to me, I imagine it would oppose motion similar to friction.
 
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... Deleted, because I posted to the wrong thread.
 
This problem doesn't give me the pressure at the outlet, and it doesn't specify that it is open to the atmosphere, so I am not sure what to use.

I also do not understand the jargon ''velocity heads''. What does it mean with reference to the expression for the loss coefficient?
 
To calculate the force, I believe you only need are the flow rate (500gpm), the diameters of the entrance (4 inches) and exit (2 inches), and the fluid density (water).
 
Well that is the information given, but for my momentum balance I don't know how to account for the gravitational force in the y-direction without some information about the size of the tube, meaning I don't know the mass of the water.
 
You also don't know which end is up.
If you want to handle gravity, just prepend your answer with "Aside from supporting the weight of the plumbing and water, ...".