
The temperature distribution

Answer to Problem 4.40P
The temperature distribution
Explanation of Solution
Given information:
The velocity component of laminar flow between parallel plate in
Write the expression for energy equation for the flow.
Here, the specific volume of the fluid is
Write the expression for change of temperature with respect to time
Here, the rate of change of temperature with respect to
Since there is no change in temperature in y and z Substitute
Substitute
Substitute
Since temperature only varies in
Calculation:
Substitute
Further integrating the equation.
Substitute the boundary equation
Substitute
Further integrating the equation.
Substitute the boundary equation
Substitute
Conclusion:
The temperature distribution
Want to see more full solutions like this?
Chapter 4 Solutions
Fluid Mechanics
- "11-17 The shaft shown in Figure P11-3 was designed in Problem 10-17. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-17, design suitable bearings to support the load for at least 1E8 cycles at 1800 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with Ox = 15, 11d=0.75, and a clearance ratio of 0.001. ✓ ✓ cast-iron roller FIGURE P11-3 Shaft Design for Problems 11-17 b gear key assume bearings act as simple supports 11-19 The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-19, design suitable bearings to support the load for at least 5E8 cycles at 1200 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with Oy = 40, 1/d=0.80, and a clearance ratio of 0.002 5. gear gear key FIGURE P11-4 Shaft Design for Problems 11-19 and…arrow_forwardFor the frame below calculate the bending moment at point R. Take P=40 and note that this value is used for both the loads and the lengths of the members of the frame. 2.5P- A Q B R С 45 degrees ✗ ✗ P i 19 Кур -2P- 4PRN -P- -arrow_forwardCalculate the bending moment at the point D on the beam below. Take F=79 and remember that this quantity is to be used to calculate both forces and lengths. 15F 30F A сarrow_forwardShow work on how to obtain P2 and T2. If using any table, please refer to it. If applying interpolation method, please show the work.arrow_forwardcast-iron roller FIGURE P11-3 Shaft Design for Problems 11-17 Chapter 11 BEARINGS AND LUBRICATION 677 gear key P assume bearings act as simple supports 11-18 Problem 7-18 determined the half-width of the contact patch for a 1.575-in-dia steel cylinder, 9.843 in long, rolled against a flat aluminum plate with 900 lb of force to be 0.0064 in. If the cylinder rolls at 800 rpm, determine its lubrication condition with ISO VG 1000 oil at 200°F. R₁ = 64 μin (cylinder); R₁ = 32 μin (plate). 11-19 The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-19, design suitable bearings to support the load for at least 5E8 cycles at 1200 rpm. State all assumptions. (a) (b) Using hydrodynamically lubricated bronze sleeve bearings with ON = 40, 1/ d=0.80, and a clearance ratio of 0.002 5. Using deep-groove ball bearings for a 10% failure rate. *11-20 Problem 7-20 determined the…arrow_forwardCalculate the shear force at the point D on the beam below. Take F=19 and remember that this quantity is to be used to calculate both forces and lengths. 15F A сarrow_forward"II-1 The shaft shown in Figure P11-I was designed in Problem 10-1. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-1, design suitable bearings to support the load for at least 7E7 cycles at 1500 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with Ox = 20, 1/d=1.25, and a clearance ratio of 0.001 5. assume bearings act as simple supports FIGURE P11-1 Shaft Design for Problem 11-1 11-2 The shaft shown in Figure P11-2 was designed in Problem 10-2. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-2, design suitable bearings to support the load for at least 3E8 cycles at 2.500 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with ON=30, 1/d=1.0, and a clearance ratio of 0.002. FIGURE P11-2 Shaft Design for Problem 11-2 Table P11-1 Data for Problems assume bearings act as simple…arrow_forwardFor the frame below, calculate the shear force at point Q. Take P=13 and note that this value is used for both the loads and the lengths of the members of the frame. 1 A Q ✗ 19 KBP 2.5P- B R C 45 degrees ✗ 1 .2P- 4PhN -P→arrow_forwardCalculate the Bending Moment at point D in the frame below. Leave your answer in Nm (newton-metres) J J A 2m 2m <2m х D 不 1m X E 5m 325 Nm 4x 400N/marrow_forwardIn the beam below, calculate the shear force at point A. Take L=78 and remember that both the loads and the dimensions are expressed in terms of L. 143 1 DX A - Li 4 LhN 14LRN/m Х B 22 3 L.arrow_forwardCalculate the Shear Force at Point F on the beam below. Keep your answer in Newtons and make shear force positive to the right. A х 2m <2m E D 5m 1m Хт 325N1m 400N/m 8arrow_forwardThe normal force at C on the beam below is equal to: A ShN C X 15h N 8 ○ OkN 2.5kN 10kN ○ 12.5kN 1m Im 1m 1m;arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY