Fittings and adapters are simple components used in piping networks to connect various forms of pipes or tubes of different sizes, shapes, and orientations. As mechanical engineers, we know that fittings disturb the flowing fluid and cause minor losses; in other words, pressure drops. The manufacturers well document the loss coefficients of the fittings to make it possible to design complex piping networks with dozens of fittings in a straightforward. Suppose that you are a design engineer, and determining the pressure drop across a fittings component is defined on you. As a first step, here we consider one of the simplest fittings components, 90° elbow. In a dedicated setup, the elbow connects the horizontal and vertical tubes with an inner diameter of 10 cm. The elbow is leaned to a support element to measure the reacting forces (horizontal and vertical components) that arise from changing the direction of the flowing fluid within the elbow. You have carefully checked the standard measurement techniques for such systems and placed two pressure sensors on the horizontal and vertical pipes. In standards, it is suggested to place the sensors on the flanges, where the elbow is connected to the main pipeline. Suppose th

2. Fittings and adapters are simple components used in piping networks to connect various forms of pipes or tubes of different sizes, shapes, and orientations. As mechanical engineers, we know that fittings disturb the flowing fluid and cause minor losses; in other words, pressure drops. The manufacturers well document the loss coefficients of the fittings to make it possible to design complex piping networks with dozens of fittings in a straightforward. Suppose that you are a design engineer, and determining the pressure drop across a fittings component is defined on you. As a first step, here we consider one of the simplest fittings components, 90° elbow. In a dedicated setup, the elbow connects the horizontal and vertical tubes with an inner diameter of 10 cm. The elbow is leaned to a support element to measure the reacting forces (horizontal and vertical components) that arise from changing the direction of the flowing fluid within the elbow. You have carefully checked the standard measurement techniques for such systems and placed two pressure sensors on the horizontal and vertical pipes. In standards, it is suggested to place the sensors on the flanges, where the elbow is connected to the main pipeline. Suppose that water is used in the test system and the volume of the elbow is 0.2 m^3. You may assume that the weight of the elbow is negligible for the selected material and the thickness wall. A magnetic flow meter is used in the system to monitor the volumetric flow rate of the working fluid during the experiments. The measurements reveal that when the water flow rate is set to 100 L/s, the horizontal and vertical forces acting on the support element are identical and measured to be 16 kN. The pump directs the working fluid from the horizontal to vertical direction through the elbow. Sketch the problem, indicate control volume, list the reasonable assumptions, define the balance equations, go through the step-by-step calculations and determine the pressure readings at the inlet and outlet of the elbow? Please double-check your calculation to ensure the validity of the results.