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A horizontal beam of length 6 meters and cross - sectional area 0 . 1 m ^ 2 is subjected to a uniformly distributed load

A horizontal beam of length 6 meters and cross-sectional area 0.1 m^2 is subjected to a uniformly distributed load of 20 kN/m. Calculate the reactions at the supports, the maximum bending moment in the beam, and the maximum deflection at the center.A hydraulic cylinder has a piston diameter of 100 mm and a rod diameter of 50 mm. If a force of 50 kN is applied to the piston, calculate the pressure exerted on the piston and rod, the force exerted by the rod, and the extension of the rod if the modulus of elasticity for the material is 200 GPa.A centrifugal pump operates at 1500 rpm and delivers water with a density of 1000 kg/m^3 at a flow rate of 0.02 m^3/s. If the pump head is 20 meters, calculate the power developed by the pump, the efficiency of the pump if the brake power is 5 kW, and the specific speed of the pump.An air compressor compresses air from 1 bar and 25C to 8 bar. Calculate the work done during compression, the heat transfer during compression if the compressor efficiency is 80%, and the final temperature of the air assuming ideal gas behavior.Calculate the velocity of a fluid flowing through a pipe of diameter 0.2 m and length 10 m if the flow rate is 0.1 m^3/s. Determine the Reynolds number for the flow and the friction factor using the Darcy-Weisbach equation.
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