Answer :
To calculate the pressures and flow rates in the given piping system, we need to apply the principles of fluid mechanics and use the continuity equation and the Bernoulli equation.
To determine the pressures and flow rates in the piping system, we can start by applying the continuity equation, which states that the mass flow rate is constant within an incompressible fluid system. Given the flow rate of 500 m²/h, we can use this equation to calculate the flow velocities in each section.
Next, we can apply the Bernoulli equation, which relates the pressure, velocity, and elevation of a fluid in a steady flow. By considering the different sections and the fact that there is no elevation change, we can calculate the pressures at various points in the system.
In section A, with a 200 mm diameter, we can use the flow velocity and diameter to calculate the flow rate. With the known flow rate and diameter of section C, we can calculate the flow velocity in that section as well.
For section B, which consists of two parallel pipes with different diameters, we can calculate the flow rates in each pipe using the flow velocities and diameters. By summing the flow rates in the two pipes, we obtain the total flow rate in section B.
Using the calculated flow rates and the Bernoulli equation, we can determine the pressures at different points in the system, considering the changes in diameter and length.
Overall, by applying the principles of fluid mechanics and using the continuity equation and Bernoulli equation, we can calculate the pressures and flow rates in the given piping system at the specified flow rate and conditions.
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