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Problem 2: Compressible flow in a pipe - as a root finding problem In a fluid mechanics course you might come across the Weymouth equation, which is used for relating the pressure drop vs. flow rate in a pipeline carrying compressible gases. It is given by, 0.5 2. = 433.541 [(P P;) d2.6677 PO (2) LOT where Q. is the gas flow rate = 2000000 SCFD T, is the standard temperature = 520R P, is the standard pressure = 14.7 psia Pi is the upstream pressure, (?), psia P, is the downstream pressure, (21.7), psia L is the length of pipe = 0.1894 miles o is the specific gravity of gas (air=1) = 0.7 T is the actual gas temperature = 530R d is the diameter of the pipe, (?) inches n is the efficiency = 0.7 (a fudge factor!) a) If the diameter of the pipe is 4.026 inches, determine the upstream pressure using the secant function initial guess of [5, 45]) and the MATLAB built-in function fzero initial guess of 25). b) Suppose the maximum pressure the pipeline can withstand is only 24.7 psia. Other conditions remaining the same as in previous part, determine the diameter of the pipe that should be used using the secant function (initial guess of [4, 8]) and the MATLAB built-in function - fzero (initial guess of 6). Problem 2: Compressible flow in a pipe - as a root finding problem In a fluid mechanics course you might come across the Weymouth equation, which is used for relating the pressure drop vs. flow rate in a pipeline carrying compressible gases. It is given by, 0.5 2. = 433.541 [(P P;) d2.6677 PO (2) LOT where Q. is the gas flow rate = 2000000 SCFD T, is the standard temperature = 520R P, is the standard pressure = 14.7 psia Pi is the upstream pressure, (?), psia P, is the downstream pressure, (21.7), psia L is the length of pipe = 0.1894 miles o is the specific gravity of gas (air=1) = 0.7 T is the actual gas temperature = 530R d is the diameter of the pipe, (?) inches n is the efficiency = 0.7 (a fudge factor!) a) If the diameter of the pipe is 4.026 inches, determine the upstream pressure using the secant function initial guess of [5, 45]) and the MATLAB built-in function fzero initial guess of 25). b) Suppose the maximum pressure the pipeline can withstand is only 24.7 psia. Other conditions remaining the same as in previous part, determine the diameter of the pipe that should be used using the secant function (initial guess of [4, 8]) and the MATLAB built-in function - fzero (initial guess of 6)