03_piston - 1 On Choosing and Using Control Volumes: Six...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 On Choosing and Using Control Volumes: Six Ways of Applying the Integral Mass Conservation Theorem to a Simple Problem Ain A. Sonin, MIT 2001, 6 pages Reference : Ain A. Sonin, Fundamental Laws of Motion for Particles, Material Volumes, and Control Volumes , 2001 We shall use a very simple example to illustrate the variety of ways in which a control volume theorem can be applied to a particular application, depending on the choice of control volume and which of the two alternative forms of the control volume theorem is used. The exercise provides a few basic insights into the thought processes that are used in control volume analysis. Figure 1 depicts something like a cylindrical syringe, or a grease gun, in which a solid piston of radius R 1 is pushed at a speed U(t) into a fluid-filled cylinder with the same internal radius, forcing the fluid out through a tube with internal radius R 2 and length L . The piston, cylinder, and tube are inflexible and made of material with density s ; the fluid has density and can be considered incompressible. Fig. 1: The system and the control volume (broken red line) for Methods 1 and 2. This control volume is fixed in the inertial reference frame of the cylinder. 2 Given the aforementioned quantities, what is the average flow speed V(t) of the fluid at the exit plane? The governing principle is clearly mass conservation, which can be written for a control volume in two alternative forms, Form A d dt dV CV ( t ) + v rn dA = CS ( t ) (1) Form B t CV ( t ) dV + v n dA = CS ( t ) (2) where v n = r v r n = v cos is the outward normal velocity component of the fluid at the control surface, and v rn = v v v v c ( ) v n is the outward normal component of the fluid...
View Full Document

This note was uploaded on 02/27/2012 for the course MECHANICAL 2.25 taught by Professor Garethmckinley during the Fall '05 term at MIT.

Page1 / 6

03_piston - 1 On Choosing and Using Control Volumes: Six...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online