1. The variation of fluid pressure with height is described bythe differential e

Question

1. The variation of fluid pressure with height is described bythe differential equation                            dP/d z = - g Hence, (rho) is specific density and g is the localacceleration of gravity. For an ideal gas, = MP / RT, whereM is molar mass and R is the universal gas constant. Modeling theatmosphere as an isothermal column of ideal gas at 10 degreescentigrade, estimate the ambient pressure in Denver, where z =1(mile) relative to sea level. For air, take M = 29 g mol^-1;values of R are given in App. A. 1. The variation of fluid pressure with height is described bythe differential equation                            dP/d z = - g Hence, (rho) is specific density and g is the localacceleration of gravity. For an ideal gas, = MP / RT, whereM is molar mass and R is the universal gas constant. Modeling theatmosphere as an isothermal column of ideal gas at 10 degreescentigrade, estimate the ambient pressure in Denver, where z =1(mile) relative to sea level. For air, take M = 29 g mol^-1;values of R are given in App. A.

Explanation / Answer

dP/dz = - g = -MPg/RT = -(29*10-3 kg/mol * 9.81m/s2/(8.31 J/mol-K * 283 K)) P = -(1.21*10-4m-1) P dP/P = -(1.21*10-4 m-1) dz integrate, lnP = -(1.21*10-4 m-1) z + lnC P = C*exp[-(1.21*10-4 m-1) z] at z = 0, P = 1.013*105 Pa so C = 1.013*105 Pa at z = 1 mile = 1609 m P = 1.013*105 Pa *exp[-(1.21*10-4m-1) * 1609 m] = 8.34*104 Pa

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