A part of a lubrication system consists of two circular disks between which a lubricant flows...
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A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In- A part of a lubrication system consists of two circular disks between which a lubricant flows radially. The flow takes place because of a pressure drop Ap between the inner and outer radii r, and r,. The system is sketched in Fig. 3.6-1. a. Write the equations of continuity and motion for the flow system, assuming steady, laminar, incompressible Newtonian flow. Consider only the region r, <r<rand assume that the flow is directed radially so that g= v, = 0. b. Show how the equation of continuity enables one to simplify the equation of motion to give (3.K-1) r de in which o= ru, is a function of z only. Why is ø independent of r? c. It can be shown that no solution exists for Eq. 3.K-1 unless the nonlinear term (that is, the term containing ) is neglected; for the proof, see Problem 3.Y. Omission of the 4* term corresponds to the "creeping flow" assumption made in deriving Stokes's law for flow around a sphere in $2.6. Show that when the nonlinear term is discarded, the equation of motion can be integrated to give: d4 0 = Ap +(u In de (3.К-2) d. Show that Eq. 3.K-2 leads to the velocity profile vdr, 2) 2ur In- 1- (3.K-3) e. Finally show that the volume rate of flow Q (in ft sec-) through the slit is given by (3.K-4) 3u In-
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Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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