Question

A venturi is a pipe-like device with a smooth internal constriction, as shown below. Air flows (20 pts) through a particular venturi, entering with know velocity (V~ ), temperature (T), and pressure (P). The venturi starts with a diameter (D), and constricts to a smaller diameter (d). A small barometer-like tube is attached to the venturi at its constriction, and filled with oil of known density (?oil). Answer the following questions about this system using the information in data table. (a) Compute the air’s density (?air) at the venturi inlet. Assume this density is constant and known; it may be used in subsequent questions as such. (b) Develop an expression for the air pressure (Pd) at the venturi’s constriction using only the provided quantities. (c) Develop an expression for the expected oil column height (?z) resulting from the density variation. The oil at the base of the barometer-like tube is also P?. (d) Numerically compute the oil column height (?z) using the derived expressions. Parameter Variable Units Value Venturi diameter D m 0.15 Venturi diameter d m 0.03 Air inlet velocity V m/s 9.3 Air inlet temperature T C 17.5 Air inlet pressure P? kPa 103.0 Air constriction pressure Pd kPa - Air inlet density ?air kg/m3 - Air gas constant Rg J/kg·K 287.057 Oil density ?oil kg/m3 780.0 Oil column height ?z m - Gravity g m/s 2 9.81

Answer 1