
Consider the incompressible viscous flow of air between two infinitely long parallel plates separated by a distance h. The bottom plate is stationary. and the top plate is moving at the constant velocity u. in the direction of the plate. Assume that no pressure gradient exists in the flow direction.
a. Obtain an expression for the variation of velocity between the plates.
b. If
(a)

The expression for the variation of velocity between the plates.
Answer to Problem 15.1P
The expression for the variation of velocity between the plates is
Explanation of Solution
Given:
The distance between the plates is
The velocity of the top plate is
Formula used:
The expression for the pressure gradient is given as,
Here,
Calculation:
The figure (1) is showing the incompressible flow of air between two infinitely long plates,
Figure (1)
The given flow is in the x direction only and the no pressure gradient in the direction of flow,
The expression for the pressure gradient is given as,
Substitute the value of pressure gradient,
Integrate the above expression,
Again integrate the above expression,
Apply boundary condition at
Substitute the values in equation (1)
At
Substitute the values in equation (1),
Substitute the values of
Conclusion:
Therefore, the expression for the variation of velocity between the plates is
(b)

The shear stress on the top and the bottom plates.
Answer to Problem 15.1P
The shear stress on the top and the bottom plates is
Explanation of Solution
Given:
The temperature of the fluid is
The velocity of the top plate is
The distance between the plates is
Formula used:
The expression to calculate the shear stress is given as,
Here,
The expression of the relation between the viscosity and the temperature is given as,
Here,
Calculation:
It is known that the value of
The expression of the relation between the viscosity and the temperature is given as,
Substitute the values in above expression
The expression to calculate the stress is given as,
Substitute the values from equation (2),
Substitute the values in above expression,
The value of shear stress is constant. Thus, the shear stress will be same on top and bottom of the plates.
Conclusion:
Therefore, the shear stress on the top and the bottom plates is
Want to see more full solutions like this?
Chapter 15 Solutions
Fundamentals of Aerodynamics
- ||! Sign in MMB241 - Tutorial L9.pd X PDF MMB241 - Tutorial L10.pX DE MMB241 - Tutorial L11.p x PDF Lecture W12 - Work and X File C:/Users/KHULEKANI/Desktop/mmb241/MMB241%20-%20Tutorial%20L11.pdf PDE Lecture W11 - Power and X Draw Alla | Ask Copilot ++ 3 of 3 | D 6. If the 50-kg load A is hoisted by motor M so that the load has a constant velocity of 1.5 m/s, determine the power input to the motor, which operates at an efficiency € = 0.8. 1.5 m/s 2 7. The sports car has a mass of 2.3 Mg, and while it is traveling at 28 m/s the driver causes it to accelerate at 5m/s². If the drag resistance on the car due to the wind is FD= 0.3v²N, where v is the velocity in m/s, determine the power supplied to the engine at this instant. The engine has a running efficiency of P = 0.68. 8. If the jet on the dragster supplies a constant thrust of T-20 kN, determine the power generated by the jet as a function of time. Neglect drag and rolling resistance, and the loss of fuel. The dragster has a mass of 1…arrow_forwardQ | Sign in PDE Lecture W09.pdf PDF MMB241 - Tutorial L9.pdi X PDF MMB241 - Tutorial L10.p X PDF MMB241 - Tutorial L11.p X Lecture W12-Work and X + File C:/Users/KHULEKANI/Desktop/mmb241/Lecture%20W12%20-%20Work%20and%20Energy.pdf ||! Draw | IA | a | Ask Copilot Class Work + 33 of 34 D Question 1 The engine of a 3500-N car is generating a constant power of 50 hp (horsepower) while the car is traveling up the slope with a constant speed. If the engine is operating with an efficiency of € 0.8, determine the speed of the car. Neglect drag and rolling resistance. Use g 9.81 m/s² and 1 hp = 745.7 W. 10 го Question 2 A man pushes on a 60-N crate with a force F. The force is always directed downward at an angle of 30° from the horizontal, as shown in the figure. The magnitude of the force is gradually increased until the crate begins to slide. Determine the crate's initial acceleration once it starts to move. Assume the coefficient of static friction is μ = 0.6, the coefficient of kinetic…arrow_forwardstate is Derive an expression for the volume expansivity of a substance whose equation of RT P = v-b a v(v + b)TZ where a and b are empirical constants.arrow_forward
- For a gas whose equation of state is P(v-b)=RT, the specified heat difference Cp-Cv is equal to which of the following (show all work): (a) R (b) R-b (c) R+b (d) 0 (e) R(1+v/b)arrow_forwardof state is Derive an expression for the specific heat difference of a substance whose equation RT P = v-b a v(v + b)TZ where a and b are empirical constants.arrow_forwardTemperature may alternatively be defined as T = ди v Prove that this definition reduces the net entropy change of two constant-volume systems filled with simple compressible substances to zero as the two systems approach thermal equilibrium.arrow_forward
- Using the Maxwell relations, determine a relation for equation of state is (P-a/v²) (v−b) = RT. Os for a gas whose av Tarrow_forward(◉ Homework#8arrow_forwardHomework#8arrow_forwardBox A has a mass of 15 kilograms and is attached to the 20 kilogram Box B using the cord and pulley system shown. The coefficient of kinetic friction between the boxes and surface is 0.2 and the moment of inertia of the pulley is 0.5 kg * m^ 2. After 2 seconds, how far do the boxes move? A бро Barrow_forwardBox A has a mass of 15 kilograms and is attached to the 20 kilogram Box B using the cord and pulley system shown. The coefficient of kinetic friction between the boxes and surface is 0.2 and the moment of inertia of the pulley is 0.5 kg * m^2. Both boxes are 0.25 m long and 0.25 m high. The cord is attached to the bottom of Box A and the middle of box B. After 2 seconds, how far do the boxes move? A From бро Barrow_forwardHomework#8arrow_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