Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2, Problem 66P
A cross section of a rotating bearing is shown. The spherical member rotates with angular speed ω, a small distance, a, above the plane surface. The narrow gap is filled with viscous oil, having μ = 1250 cp. Obtain an algebraic expression for the shear stress acting on the spherical member. Evaluate the maximum shear stress that acts on the spherical member for the conditions shown. (Is the maximum necessarily located at the maximum radius?) Develop an algebraic expression (in the form of an integral) for the total viscous shear torque that acts on the spherical member. Calculate the torque using the dimensions shown.
P2.66
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Water flows through a horizontal, 180 pipe bend as shown in figures. The flow cross-sectional area is constant at a value of 0.1 ft2 through the bend. The magnitude of the flow velocity everywhere in the bend is 50ft/s. The hydrostatic pressures at the entrance and exit of the bend are 30 psi and 24 psi, respectively. Calculate the horizontal and vertical components of the anchoring force required to hold the bend in place.
The block of weight W = 50 N is pulled by a weight W0 = 60 N along the surface of a table by means of an inextensible cable and a pulley. Between the block and the table there is a uniform layer of oil of viscosity m = 0.1 Pa-s and clearance h = 2 mm. The contact area is 0.01 m2. Find the terminal velocity U if the table is very long.
Two very large open tanks A and F (Fig. ) containthe same liquid. A horizontal pipe BCD, having a constriction at C andopen to the air at D, leads out of the bottom of tank A, and a verticalpipe E opens into the constriction at C and dips into the liquid in tank F.Assume streamline flow and no viscosity. If the cross-sectional area atC is one-half the area at D and if D is a distance h1 below the level ofthe liquid in A, to what height h2 will liquid rise in pipe E? Express youranswer in terms of h1.
Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - A viscous liquid is sheared between two parallel...Ch. 2 - For the velocity field V=Ax2yi+Bxy2j, where A = 2...Ch. 2 - A fluid flow has the following velocity...Ch. 2 - When an incompressible, nonviscous fluid flows...Ch. 2 - For the free vortex flow the velocities are t =...Ch. 2 - For the forced vortex flow the velocities are t =...Ch. 2 - A velocity field is specified as V=axyi+by2j,...Ch. 2 - A velocity field is given by V=ax3i+bxy3j, where a...
Ch. 2 - The velocity for a steady, incompressible flow in...Ch. 2 - The flow field for an atmospheric flow is given by...Ch. 2 - For the velocity field V=AxiAyj,, where A = 2s 1....Ch. 2 - A velocity field in polar coordinates is given...Ch. 2 - The flow of air near the Earths surface is...Ch. 2 - A velocity field is given by V=aytibxj, where a =...Ch. 2 - Air flows downward toward an infinitely wide...Ch. 2 - Consider the flow described by the velocity field...Ch. 2 - Consider the velocity field V = axi + by(1 + ct)...Ch. 2 - Consider the flow field given in Eulerian...Ch. 2 - A velocity field is given by V=axti+byj, where A =...Ch. 2 - Consider the garden hose of Fig. 2.5. Suppose the...Ch. 2 - Consider the velocity field of Problem 2.18. Plot...Ch. 2 - Streaklines are traced out by neutrally buoyant...Ch. 2 - Consider the flow field V=axti+bj, where a = 1/s2...Ch. 2 - A flow is described by velocity field V=ay2i+bj,...Ch. 2 - Tiny hydrogen bubbles are being used as tracers to...Ch. 2 - A flow is described by velocity field V=ai+bxj,...Ch. 2 - A flow is described by velocity field V=ayi+btj,...Ch. 2 - A flow is described by velocity field V=ati+bj,...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - Some experimental data for the viscosity of helium...Ch. 2 - The velocity distribution for laminar flow between...Ch. 2 - What is the ratio between the viscosities of air...Ch. 2 - Calculate velocity gradients and shear stress for...Ch. 2 - A very large thin plate is centered in a gap of...Ch. 2 - A female freestyle ice skater, weighing 100 lbf,...Ch. 2 - A block of mass 10 kg and measuring 250 mm on each...Ch. 2 - A 73-mm-diameter aluminum (SG = 2.64) piston of...Ch. 2 - A vertical gap 25 mm wide of infinite extent...Ch. 2 - A cylinder 8 in. in diameter and 3 ft long is...Ch. 2 - Crude oil at 20C fills the space between two...Ch. 2 - The piston in Problem 2.40 is traveling at...Ch. 2 - A block of mass M slides on a thin film of oil....Ch. 2 - A block 0.1 m square, with 5 kg mass, slides down...Ch. 2 - A torque of 4 N m is required to rotate the...Ch. 2 - A circular disk of diameter d is slowly rotated in...Ch. 2 - The fluid drive shown transmits a torque T for...Ch. 2 - A block that is a mm square slides across a flat...Ch. 2 - In a food-processing plant, honey is pumped...Ch. 2 - SAE 10W-30 oil at 100C is pumped through a tube L...Ch. 2 - The lubricant has a kinematic viscosity of 2:8105...Ch. 2 - Calculate the approximate viscosity of the oil....Ch. 2 - Calculate the approximate power lost in friction...Ch. 2 - Fluids of viscosities 1 = 0.1 Ns/m2 and 2 = 0.15...Ch. 2 - A concentric cylinder viscometer may be formed by...Ch. 2 - A concentric cylinder viscometer is driven by a...Ch. 2 - A shaft with outside diameter of 18 mm turns at 20...Ch. 2 - A shock-free coupling for a low-power mechanical...Ch. 2 - A proposal has been made to use a pair of parallel...Ch. 2 - The cone and plate viscometer shown is an...Ch. 2 - A viscometer is used to measure the viscosity of a...Ch. 2 - A concentric-cylinder viscometer is shown. Viscous...Ch. 2 - Design a concentric-cylinder viscometer to measure...Ch. 2 - A cross section of a rotating bearing is shown....Ch. 2 - Small gas bubbles form in soda when a bottle or...Ch. 2 - You intend to gently place several steel needles...Ch. 2 - According to Folsom [6], the capillary rise h...Ch. 2 - Calculate and plot the maximum capillary rise of...Ch. 2 - Calculate the maximum capillary rise of water...Ch. 2 - Calculate the maximum capillary depression of...Ch. 2 - Water usually is assumed to be incompressible when...Ch. 2 - The viscous boundary layer velocity profile shown...Ch. 2 - In a food industry process, carbon tetrachloride...Ch. 2 - What is the Reynolds number of water at 20C...Ch. 2 - A supersonic aircraft travels at 2700 km/hr at an...Ch. 2 - SAE 30 oil at 100C flows through a 12-mm-diameter...Ch. 2 - A seaplane is flying at 100 mph through air at...Ch. 2 - An airliner is cruising at an altitude of 5.5 km...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A 150 mm horizontal waterline contracts abruptly to 75 mm diameter. A pressure gage 150 mm upstream from the contraction reads 34.5 kPa when the mean velocity in the 150 mm pipe is 1.5 m/s. What will pressure gages read 0.6 m downstream and just downstream from the contraction if the diameter of the vena contracta is 61 mm? Neglect pipe frictionarrow_forwardAn instrument popular in the beverage industry is the targetflowmeter in Fig. A small flat disk is mountedin the center of the pipe, supported by a strong but thin rod.(a) Explain how the flowmeter works. (b) If the bendingmoment M of the rod is measured at the wall, derive a formulafor the estimated velocity of the flow. (c) List a fewadvantages and disadvantages of such an instrument.arrow_forwardsolve a and b. A shaft 80 mm in diameter is being pushed through a bearing sleeve 80.2mm in diameter and 0.3 m long. The clearance, assumed uniform is flooded with lubricating oil of viscosity 0.1 kg/ms. (a) If the shaft moves axially at 0.8 m/s, estimate the resistance force exerted by the oil on the shaft, (b) If the shaft is axially fixed and rotated at 1800 rpm, estimate the resisting torque exerted by the oil and the power required to rotate the shaft.arrow_forward
- The rotating parts of a hydroelectric power plant having power capacity W . have a rotational synchronous speed n .. The weight of the rotating parts (the hydroturbine and its electric generator) is supported in a thrust bearing having annular form between D and d diameters as sketched. The thrust bearing is operated with a very thin oil film of thickness e and dynamic viscosity ? . It is assumed that the oil is a Newtonian fluid and the velocity is approximated as linear in the bearing. Calculate the ratio of lost power in the thrust bearing to the produced power in the hydraulic power plant. Use W . = 48.6 MW, ? = 0.035 Pa⋅s, n . = 500 rpm, e = 0.25 mm, D = 3.2 m, and d = 2.4 m.arrow_forwardDescribe the forces that enable the submarine to descend or ascend in the seawater. When the submarine holds at the constant depth of 3,500m, calculate the buoyant force on the submarine. weight of seawater in the ballast tank. seawater pressure. When seawater flows into the bottom opening at 10 m/s, calculate the velocity of the seawater level (8m above the bottom of the submarine) inside the ballast tank (v on diagram). Calculate the net force on the submarine circular hatch door (10m above the bottom of the submarine) with a radius of 0.5m. The air pressure inside the submarine below the hatch door is 150 101.3 kPa. Calculate the change in heat energy of the submarine’s outer haul, when it descends from the surface to a depth of 3,500m (with an average temperature of 20°C). Calculate the power of the submarine’s electrical heater needed, to maintain the interior of outer hull at 30°C. The exterior of outer hull is 10°C. (Assume heat of the submarine…arrow_forwardThe viscosity of clover honey is listed as a function of temperature. The specific gravity of the honey is about 1.42 and is not a strong function of temperature. The honey is squeezed through a small hole of diameter D = 6.0 mm in the lid of an inverted honey jar. The room and the honey are at T = 20°C. Estimate the maximum speed of the honey through the hole such that the flow can be approximated as creeping flow. (Assume that Re must be less than 0.1 for the creeping flow approximation to be appropriate.) Repeat your calculation if the temperature is 50°C. Discuss.arrow_forward
- A horizontal pipe of diameter 25cm has a constriction of diameter of 5cm. The velocity of the water in the pipe is 1cm/s and the pressure is 10⁵ Pa. Calculate the velocity and pressure in the constriction. Include an illustration or drawing of the situationarrow_forwardThe diameter of a pipeline is 6-in at A and 18-in at B. A is 11 ft. lower than B. If the pressure at A is 10 lb per sq. in and at B 7 lb per sq. in when the flow is 2.5 cfs, determine the frictional loss between A and B when the liquid is water. Topic: FUNDAMENTALS OF FLUID FLOWarrow_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_forward
- A liquid with negligible viscosity flows through the pipe as shown. This is an overhead view.a. Rank in order, from largest to smallest, the flow speeds v1 to v4 at points 1 to 4. Explain.b. Rank in order, from largest to smallest, the pressures p1 to p4 at points 1 to 4. Explain.arrow_forwardH.W:A piece of the pipe 300 mm long weighing 13 N and having i.d of 51mm is slipped over a vertical shaft 50 mm in diameter and allowed to fall .calculate the approximate velocity attained by the pipe if a film of oil of viscosity 25 pa.s is maintained between pipe and shaft .arrow_forwardUsing the following streamline pattern, draw an appropriate control volume on the topside of the airfoil and describe how the airfoil creates a lift force based on the equations for conservation of mass and momentum.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended 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 Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license