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
- A hydraulic ram 200 mm in diameter and 1.2 m long moves wholly within a concentric cylinder 200.2 mm in diameter, and the annular clearance is filled with oil of relative density 0.85 and kinematic viscosity 400 mm2/s. What is the viscous force resisting the motion when the ram moves at 120 mm/s?arrow_forwardDetermine the velocity profile within a 12 µm diameter capillary, with a viscosity of 4 cP, and a pressure gradient of 25 mm Hg/500 µm. Assume that gravitational effects can be ignored and that the blood vessel is perfectly cylindrical.arrow_forwardAssume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider a venturi with a small hole drilled in the side of the throat. Thishole is connected via a tube to a closed reservoir. The purpose of theventuri is to create a vacuum in the reservoir when the venturi is placed inan airstream. (The vacuum is defined as the pressure difference below theoutside ambient pressure.) The venturi has a throat-to-inlet area ratio of0.85. Calculate the maximum vacuum obtainable in the reservoir when theventuri is placed in an airstream of 90 m/s at standard sea level conditions.arrow_forward
- The hydrogen bubbles that produced the velocity profilesin Fig. are quite small, D ≈0.01 mm. If the hydrogen–water interface is comparable to air–water and the watertemperature is 30 ° C, estimate the excess pressure withinthe bubble.arrow_forwardFind the kinematic viscosity of an oil having density of 980kg/m^2 when at a certain point in the oil, the shear stress is 0.25 Pa and the velocity gradient is 0.3 m/s.arrow_forwardA pipe inclined at 45° to the horizontal (Fig. 2) converges over a length l of 2 m from a diameterd1 of 200 mm to a diameter d2 of 100 mm at the upper end. Oil of relative density 0.9 flowsthrough the pipe at a mean velocity ?̅1 at the lower end of 2 m/s. Find the pressure differenceacross the 2 m length ignoring any loss of energy, and the difference in level that would beshown on a mercury manometer connected across this length. The relative density of mercury is 13.6 and the leads to the manometer arefilled with the oil.arrow_forward
- 04/13/2021 For this exercise Study and Derive the Bernoulli equation starting with the application of Newton’s second law to a fluid particle.arrow_forwardAir at 20°C and 1 atm flow at 20 m/s past the flat platein Fig. . A pitot stagnation tube, placed 2 mm fromthe wall, develops a manometer head h = 16 mm of Meriamred oil, SG = 0.827. Use this information to estimatethe downstream position x of the pitot tube. Assumelaminar flow.arrow_forwardConsider steady flow of water through an axisymmetric garden hose nozzle. Along the centerline of the nozzle, the water speed increases from uentrance to uexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle, calculate the fluid acceleration along the nozzle centerline as a function of x and the given parameters.arrow_forward
- The belt in the Ögure moves at steady velocity V and skims the top of a tank of oil having viscosity. (a) Develop and expression for the required belt drive power in terms of h, L, b, V , and . Recalthat, for steady motion, power is equal to force velocity.(b) What power is required if the belt moves at 5 m/s over SAE 50W oil ( = 0:86 kg/ms) withh = 2 cm, L = 2 m, and b = 0:5 marrow_forwardWater at 20°C flows past a 1-m-diameter circular cylinder.The upstream centerline pressure is 128,500 Pa. If the lowestpressure on the cylinder surface is exactly the vaporpressure, estimate, by potential theory, the stream velocity.arrow_forwardA solid cone of angle 2θ, mass (m), base radius (r0), and density (ρc), is rotating with angular velocity (w0) on its conical seat. The clearance (h) is filled with oil of viscosity (μ). Neglecting air resistance, determine: a) an expression for the moment (M) as a function of r0, w0,μ,θ, and h. b) an expression for the angular velocity (w) for t≥0 as a function of w0,μ,θ,h, r0,m and t if an external torque is not applied. If the radius of gyration of the cone is 16 cm, determine: c ) the value of the angular momentum and velocity if w0=60RPM,h=0.05mm,θ=30°,μ=0.98cPoise , m=20kg, t=2.0sarrow_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