Given is the velocity of the airflow (v), temperature (T), and pressure (P) as v= 680 m/s, T= 288 K, and P= 1.01 N/m² respectively. We are required to calculate the following quantities:
Total temperatureTotal pressureTotal densityTotal enthalpyFlow Mach numbera.
Total temperatureThe total temperature is given by:Tt = T + (v²/2*Cp)Where, Cp is the specific heat at constant pressureCp = 1005 J/kg-KTt = 288 + ((680²)/(2*1005))= 1001.86 Kb. Total pressureThe total pressure is given by:Pt = P*(1+(γ-1)/2*(Mach)²)^(γ/γ-1)Where, γ is the ratio of the specific heat of the gas= 1.4Mach is the Mach number Pt = 1.01*(1+(1.4-1)/2*(680/343)^2)^(1.4/1.4-1)= 1.287 N/m²c. Total densityThe total density is given by:ρt = P/((R/M)*Tt)Where, R is the specific gas constant= 287 J/kg-KM is the molar mass of the gas= 28.96 gm/molρt = 1.01/((287/28.96)*1001.86)= 0.372 kg/m³d. Total enthalpyThe total enthalpy is given by:Ht = Cp*TtHt = 1005*1001.86= 1,008,300 J/ke. Flow Mach numberThe Mach number is given by:Mach = v/aWhere, a is the speed of sound in the gas. a = √(γ*R*T) = 343 m/sMach = 680/343= 1.98Therefore, the Total Temperature is 1001.86 K.The Total Pressure is 1.287 N/m².The Total Density is 0.372 kg/m³.The Total Enthalpy is 1,008,300 J/ke.The Flow Mach Number is 1.98.