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 and Applications
- 3. A cubical block weighing 20 kg and having a 20 cm edge is allowed to slide down an inclined plane making an angle of 20° with the horizontal on which there is a thin film of oil having viscosity 0.22 N.s/m2. What velocity will be attained by the block if the film thickness is estimated to be 0.025 mm?arrow_forwardA steel ball with the density of 6229 kg/m and the radius of 0,65 cm was dropped into the oil whose viscosity was to be measured as isseen in the figure. When the ball attains a constant velocity, the distance that the ball travelled was measured as 99 cm within the time interval of 4,7 sec. Before the experiment, the mass of the 100 ml-oil was measured as 2,1 gr. According to the data given above, find; a) the density of the oil (in kg/m ). (Please do not use any decimal digit.) b) the speed of the steel ball after the ball attains a constant velocity (in m/s). (Please use 4 decimal digits.) c) the dynamic viscosity of the oil (in Pa.s) (Please use 3 decimal digits.) d) the flow Reynolds number. (Please use 4 decimal digits.) Please solve this question step by step to reach correct answers. correct answers: a) 21 b) 0,2106 c) 2,715 d) 0,0212arrow_forwardWhat is the difference between dynamin and kinematic viscosity? That is the significance of these properties of liquid?arrow_forward
- In the study of fluid phenomena, how does Newton's Law of Viscosity affect your calculations?arrow_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_forwardA fluid between two very long parallel plates is heated in a way that its viscosity decreases linearly from 0.90 Pa⋅s at the lower plate to 0.50 Pa⋅s 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.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_forwardBernoulli's theory experiment For the application of Bernoulli’s theory, there are restricted conditions, including that the viscosity of the fluid is considered zero, that it is a non-pressurized fluid, and that the two atmospheres are one away.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
- (a) A liquid with known properties (i.e. density, viscosity, etc. ) is contained in the space Ra 0 the temperature of the outer cylinder (r = Ro) is T; > Tọ. Provide an estimate for the time required to reach steady state (i.c. the time required for the diffusion penetration to reach the surface of the inner cylinder). (b) Define the thermal diffusivity a and its units. To answer the "units question", use only the fundamental units: length L, mass M, time T and temperature e. For example, the units for the velocity are L/T (and not m/sec or miles/hour). (e) You study a problem which involves momentum and energy transfer. Under which condition(s) the problem velocity and temperature are identical, i.e. are given by the same equation if we scale both the velocity and the temperature with their corresponding scales?arrow_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_forwardWhen a fluid is flowing, the velocity gradient is equal to viscosity equal to shear stress o directly proportional to shear stress inversely proportional to shear stressarrow_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