Concept explainers
A fluid between two very long parallel plates is heated in a way that its viscosity decreases linearly from 0.90 PM at the lower plate to 0.50 PM at the upper plate. The spacing between the two plates is 0.4 mm. The upper plate moves steadily at a velocity of 10 m/s, in a direction parallel to both plates. The pressure is constant everywhere, the fluid is Newtonian, and assumed incompressible. Neglect gravitational effects. (a) Obtain the fluid velocity u as a function of y, u(y), where y is the vertical axis perpendicular to the plates. Plot the velocity profile across the gap between the plates. (b) Calculate the value of the shear stress. Show the direction of the shear stress on the moving plate and on the top surface of the fluid element adjacent to the moving plate.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
- A rectangular plate of length 15 cm and width 10 cm rests on a layer of liquid of thickness 0.8 mm. If the coefficient of viscosity of the fluid is 1600 cP, calculate the force that must be applied to the plate in the horizontal direction so that the plane moves with a velocity of 20 cm/s.arrow_forwardA compressed air tank is designed to contain 50 standard cubic feet of air when Ölled to a gaugepressure of 200 atm at an ambient temperature of 70 F. Calculate the interior volume of thetank. One standard cubic foot of air occupies one cubic foot at standard temperature and pressure(T = 59 F and p = 2116 lb/ft2).arrow_forwardThe Question is 50 mm-diameter and 100 mm-height cylinder is rotating with constant angularspeed of w= 300 rad/sec in a gap whose thickness varies linearly from 1 mm to 10 mm. The gap is filled with a fluid whose viscosity is 0.2 Ns/m2. Find the required torque that should be applied to the cylinder in order to maintain its motion.arrow_forward
- Darrow_forward2. A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 cm apart, and the medium between them is filled with oil whose viscosity is 0.9 N.s/m?. The part of the plate immersed in oil at any giventime is 2 m long and 0.5 m wide. If the plate moves through the mid-plane between the surfaces, determinethe force requuired to maintain this motion. What would your response be if the plate was 1 cm from the bottom surface (h2) and 3 cm from the top surface (h1)? 0M Stationary surface h1 V= 5 m/s Foi obta h2 de 1074 Stationary surface Fig. 2arrow_forwardAn air receiver carries a pressure of 3500 kPa absolute @ a temperature of 25 C. A fire occurs near the receiver which causes the temperature to rise to 80 C. Neglecting the increased volume of the receiver due to expansion, calculate the air pressure at this temperature.arrow_forward
- What is the Helmholtz absolute viscosity of water at 670°R? What is the weight in lbf of a liquid that has a mass of 30lbm on earth with g=32.174ft/s2? Weight in lbf if the g=29ft/s2?arrow_forwardA flat plate of area 2x10¹ cm² is pulled with a speed of 0.5 m/s relative to another plate located at a distance of 0.2 mm from it. If the fluid separated the two plates has a viscosity of 1.0 poise, find the force required to maintain the speed.arrow_forwardTwo identical thermometers made of Pyrex glass contain , respectively,identical volumes of mercury and methyl alcohol. If the expansion of the glass is taken into account, calculate how many times greater is the distance between the degree marks on the methy lalcohol thermometer than the distance on the mercury thermometer.arrow_forward
- Fluid Mechanics IIarrow_forwardTwo plates are seperated by a distance 1 mm and the gap between the plates is filled with a fluid. If the force required per unit area to move one plate with a velocity of 1 mm/s relative to another plate is 0.001 N/m?, then the dynamic viscosity of the fluid in Pa.s is, 0.01 O 0.1 O 0.00001 0.001arrow_forwardConsider a column of a planet's atmosphere. The planet's atmosphere is a compressible ideal gas at rest that obeys the polytropic relation Po %3D 3/2 Po 3/2 where pis pressure and pis density. Here, p, and P, are the values of pressure and density, respectively, at the planet's surface. Take z (altitude) to be positive upward with z=0 at the surface, take R to be the gas constant for the planet's atmosphere, and take g to be the downward acceleration due to gravity. a) Starting from hydrostatic balance and the polytropic relation above, derive an expression for the pressure field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. b) Derive an expression for the density field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. c) Derive an expression for the temperature field, T(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic.arrow_forward
- 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