Compressible Flow in a Convergent-Divergent Nozzle - Assignment Example

Name & ID Course Name & Code Instructor’s Name 12 December 2009 Table of Contents Table of Contents 2 Experiment 1 3 Introduction 3 Theory 4 Formulae used in this experiment 4 Objective 6 Experimental Procedure 6 Discussion 6 Conclusion 7 Experiment 2 8 Introduction 8 Objectives 9 Theory 9 Shear Stress 9 Mean Velocity Profile 10 Skin Friction using Clauser Plot 11 Skin Friction Using Preston Tube 11 Apparatus 12 Experiment 1 Introduction The aim of this experiment is to investigate compressible flow in a convergent-divergent nozzle. In the case of incompressible flow, the flow decelerates as it passes the divergent are and it accelerates when it passes through the convergent duct. Isentropic flow occurs in a state that is adiabatic and frictionless in which the cross sectional area is fluctuating, and the relationship between Mach number, velocity and area is given by: Where: Mach number is M Cross sectional area is  and velocity is  Changing the area of a nozzle affects its operations because from the equation above (1-M2); when M is less than one (M < 1), the results is positive thus the flow is subsonic while when M is greater than one (M > 1) the result will be negative and thus the flow is supersonic. However, when M is equal to one (M=1), the left part of the equation will be zero hence the right side will be zero; dA=dV=0. Changing the area of the nozzle affects differently both subsonic flow and supersonic flow; when the flow accelerates in a convergent duct is called subsonic while accelerating in a divergent duct is called supersonic. Thus, when supersonic is to be created, the flow is first passed through convergent duct that accelerates at subsonic speed passes through a minimum duct area and accelerating to supersonic condition in divergent duct. However, it is important to note that supersonic condition will be reached if M=1 at the most minimal cross sectional area at the nozzle. Theory A phenomenon known as ‘chocked’ in a nozzle occurs when there is a combination of supersonic, subsonic, and where Mach number is equal to 1, and the mass flow rate reaches maximum value. Formulae used in this experiment The following equation shows the relationship that exists between stagnation and static conditions: When the flow is at rest, stagnation occurs in which it is represented with ‘o’ while the static conditions occur when the flow is in motion. For the purpose of this experiment, air is used for flow analysis in which = 1.4, so the above equation becomes: There are usually two cross-sectional area and minimum cross-sectional area will have two possible solutions because the given value of A in which one is supersonic (M>1) while the other is subsonic (M0, and dp Read More