1. Derive an equation for the reaction force (Rx) associated with conservation of momentum in a straight length of pipe of uniform diameter. Approximate the velocity as steady and uniform at each cross-section, and the fluid as constant density. Identify the forces as pressure, shear and reaction (you may neglect weight). The final equation should use the flow rate (Q) rather than the velocity. Be careful with your signs! Make sure you draw and label a diagram including the x and (if necessary) y axis directions.
2. Similar to problem 1, but for a 90 degree bend in a pipe with uniform diameter. Note that you need to write equations for both x and y directions to get equation for both Rx and Ry ! You may neglect the shear force as well as weight for this problem.
3. Similar to problem 2, but for a 180 degree bend in a pipe with uniform diameter. Here you only need to write an equation for the x direction. You may neglect the shear force as well as the weight for this problem