Concept explainers
Oil of viscosity
(a) Sketch the approximate shape of the velocity profile w(x), considering the boundary conditions at the wall and at the film surface.
(b) Suppose film thickness
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Fluid Mechanics
- Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?arrow_forwardQ.2 An incompressible fluid (kinematic viscosity, 7.4x10-7 m2, 7.4×10 m/sec, specific gravity, 0.44) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, then fluid attains a linear velocity profile in the gap of 0.5 mm between these plates. The shear stress (in Pascals) on the surface of bottom plate is 2 0.3256 N/m A 0.4256 N/m C 0.5256 N/m2 2 D 0.6256 N/marrow_forwardA shaft 70.0 mm in diameter is being pushed at speed of 0.4 m/s through a bearing sleeve 70.2 mm in diameter and 250 mm long. The clearance, assumed uniform, is filled with oil at 4degree C with viscosity of 0.005 m^2/s and s.g. =0.9. Find the force exerted on the shaft in N. a. 18,000 b. 4.50 c. 986.45 d. 989.64arrow_forward
- Q.3b Prove that the pressure 'p' is independent of the transverse coordinate 'y' in the boundary layer and hence show that the boundary layer equation for a flow over flat plate is given by, a² u ди ди u +v== 9 əx Əy Əy² where v is the kinematic viscosity of the fluid (may use 'order of magnitude' approach).arrow_forwardq1(c) A 20 × 20 cm cubical block slides on an oil surface over the inclined plane at 20° horizontal. Steady state velocity is 0.4 m/s. The thickness of the oil film between the block and the surface is 0.4 mm, and the mass of the block is 6.52 kg. (i) Illustrate the free body diagram for the above condition. (ii) Calculate the kinematic viscosity of the oil if the specific gravity of the oil that you choose must be in the range between 0.78 to 0.86.arrow_forwardA seA A, soA A solid cylinder of diameter d, length and density p, falls due to gravity inside a pipe of diameter D. The clearance between the solid cylinder and the pipe is filled with a Newtonian fluid of density p and u. For this clearance fluid, the terminal velocity of the cylinder is determined to be V, assuming a linear velocity profile. However, if the clearance fluid was changed to a Newtonian fluid of density 2p and viscosity 2u, then for an assumed linear velocity profile, the terminal velocity of the cylinder was determined to be V,. From the results of these experiments, one may write that (A) V = V (C) 2 V= V (B) V=2 V, (D) V= 4 Varrow_forward
- Example viscosities u' and u" on the two sides of the plate. The plate is pulled at a constant velocity V. Calculate the position of plate so that: ) The shear force on the two sides of the plate is equal (i) The force required to drag the plate is minimum. Assume viscous flow and neglect all end effects. A thin plate of very large area is placed in a gap of height h with oils of Position of the plate, y: Thin platearrow_forwardAsaparrow_forwardA piston having a diameter of 9in. and a length of 995in. slides downward with a velocity V through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 90000 in., and the cylinder weighs 7836lb. Estimate V if the oil kinematic viscosity is 7800 ft'/s and its density 432 slugs/ft.Assume the velocity distribution in the gap is linear.arrow_forward
- m. A piston having a diameter 0.15 m and a length of 0.25 m as shown in figure (1.2) slides downward with a velocity (V) through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 5*10° m, and the cylinder weighs 2.22 N. Estimate V if the oil viscosity is 0.016 N.s/m². Assume the velocity distribution in the gap is linear. 2. Figure (1.1) W D Figure (1.2) Scanned with CamScannerarrow_forwardA viscous incompressible liquid of density p and of dynamic viscosity n is carried upwards against gravity with the aid of moving side walls. This laminar flow is steady and fully developed in z-direction and there is no applied pressure gradient. The coordinate is fixed in the midway between the walls as shown below. 2d g=-gk liquid P, n x=-d x=d I. The velocity profile in z-direction is pg w(x) = (x2 – d) + U. 2n II. To be able to carry a net amount of liquid upwards, the wall velocities need to be greater than pgd²/(2n). III. If one of the walls stops, increasing the speed of the other wall to 3/2U would carry the same amount of liquid upwards. Which of the above statements are true?arrow_forward2. Consider a flow with the velocity profile given by the equation below. The fluid surface is located at y = 0. Here, U∞ is called the freestream velocity and 8 is called the boundary layer thickness. Calculate the boundary layer thickness at a point where the shear stress is 36 mPa if the freestream velocity is 40 m/s and the fluid's dynamic viscosity 1.81.105 Pa.s. U.. ( 2 (²) - (²) ²) u(y) = U∞oarrow_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