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Next: The Impulse Function in Up: The Impulse Function Previous: The Impulse Function Index Impulse in Isentropic Adiabatic NozzleOne of the functions that is used in calculating the forces is the Impulse function. The Impulse function is denoted here as , but in the literature some denote this function as . To explain the motivation for using this definition consider the calculation of the net forces that acting on section shown in Figure (4.9). To calculate the net forces acting in the x-direction the momentum equation has to be applied The net force is denoted here as . The mass conservation also can be applied to our control volume Combining equation (4.104) with equation (4.105) and by utilizing the identity in equation (4.42) results in Rearranging equation (4.106) and dividing it by results in Examining equation (4.107) shows that the right hand side is only a function of Mach number and specific heat ratio, . Hence, if the right hand side is only a function of the Mach number and than the left hand side must be function of only the same parameters, and . Defining a function that depends only on the Mach number creates the convenience for calculating the net forces acting on any device. Thus, defining the Impulse function as In the Impulse function when ( M=1 ) is denoted as The ratio of the Impulse function is defined as This ratio is different only in a coefficient from the ratio defined in equation (4.107) which makes the ratio a function of and the Mach number. Hence, the net force is To demonstrate the usefulness of the this function consider a simple situation of the flow through a converging nozzle Solution
Next: The Impulse Function in Up: The Impulse Function Previous: The Impulse Function Index Created by:Genick Bar-Meir, Ph.D. On: 2007-11-21 |