FLUID MECHANICS-PHYSICAL ACCESS CODE
8th Edition
ISBN: 9781264005086
Author: White
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 4, Problem 4.95P
Two immiscible liquids of equal thickness h are being sheared between a fixed and a moving plate, as in Fig. P4.95. Gravity is neglected, and there is no variation with x. Find an expression for (a) the velocity at the interface and (b) the shear stress in each fluid. Assume steady laminar flow.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
P4.88 The viscous oil in Fig. P4.88 is set into
steady motion by a concentric inner cylinder
moving axially at velocity U inside a fixed
outer cylinder. Assuming constant pressure and
density and a purely axial fluid motion, solve
Eqs. (4.38) for the fluid velocity distribution
vz(r). What
are the proper boundary conditions?
b.
v(r)
a
U
Oil: p, H
P3.5 Water at 20°C flows through a 5-in-diameter smooth pipe
at a high Reynolds number, for which the velocity profile
is approximated by u = U.(v/R)/8, where U, is the cen-
terline velocity, R is the pipe radius, and y is the distance
measured from the wall toward the centerline. If the cen-
terline velocity is 25 ft/s, estimate the volume flow rate
in gallons per minute.
An excellent approximation for the two-dimensional
incompressible laminar boundary layer on the flat surface
in Fig. P4.17 is
for y s8
where 8 = Cx2, C = const
(a) Assuming a no-slip condition at the wall, find an expression
for the velocity component v(x, y) for ys 8. (b) Then find the
maximum value of vat the station x = 1 m, for the particular
case of airflow, when U = 3 m/s and &= 1.1 cm.
Layer thickness 5(x)
U= constant
и (х, у)
u(x, y)
Chapter 4 Solutions
FLUID MECHANICS-PHYSICAL ACCESS CODE
Ch. 4 - Prob. 4.1PCh. 4 - Flow through the converging nozzle in Fig. P4.2...Ch. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - P4.8 When a valve is opened, fluid flows in...Ch. 4 - An idealized incompressible flow has the proposed...Ch. 4 - A two-dimensional, incompressible flow has the...
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - What is the most general form of a purely radial...Ch. 4 - Prob. 4.16PCh. 4 - An excellent approximation for the two-dimensional...Ch. 4 - Prob. 4.18PCh. 4 - A proposed incompressible plane flow in polar...Ch. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - An incompressible flow in polar coordinates is...Ch. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - P4.28 For the velocity distribution of Prob. 4.10,...Ch. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - Prob. 4.34PCh. 4 - P4.35 From the Navier-Stokes equations for...Ch. 4 - A constant-thickness film of viscous liquid flows...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Reconsider the angular momentum balance of Fig....Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Consider the following two-dimensional...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - P4.54 An incompressible stream function is...Ch. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - A two-dimensional incompressible flow field is...Ch. 4 - P4.58 Show that the incompressible velocity...Ch. 4 - Prob. 4.59PCh. 4 - Prob. 4.60PCh. 4 - An incompressible stream function is given by...Ch. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - A stream function for a plane, irrotational, polar...Ch. 4 - Prob. 4.68PCh. 4 - A steady, two-dimensional flow has the following...Ch. 4 - A CFD model of steady two-dimensional...Ch. 4 - Consider the following two-dimensional function...Ch. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.74PCh. 4 - Given the following steady axisymmetric stream...Ch. 4 - Prob. 4.76PCh. 4 - Prob. 4.77PCh. 4 - Prob. 4.78PCh. 4 - Prob. 4.79PCh. 4 - Oil, of density and viscosity , drains steadily...Ch. 4 - Prob. 4.81PCh. 4 - Prob. 4.82PCh. 4 - P4.83 The flow pattern in bearing Lubrication can...Ch. 4 - Consider a viscous film of liquid draining...Ch. 4 - Prob. 4.85PCh. 4 - Prob. 4.86PCh. 4 - Prob. 4.87PCh. 4 - The viscous oil in Fig. P4.88 is set into steady...Ch. 4 - Oil flows steadily between two fixed plates that...Ch. 4 - Prob. 4.90PCh. 4 - Prob. 4.91PCh. 4 - Prob. 4.92PCh. 4 - Prob. 4.93PCh. 4 - Prob. 4.94PCh. 4 - Two immiscible liquids of equal thickness h are...Ch. 4 - Prob. 4.96PCh. 4 - Prob. 4.97PCh. 4 - Prob. 4.98PCh. 4 - For the pressure-gradient flow in a circular tube...Ch. 4 - W4.1 The total acceleration of a fluid particle is...Ch. 4 - Is it true that the continuity relation, Eq....Ch. 4 - Prob. 4.3WPCh. 4 - Prob. 4.4WPCh. 4 - W4.5 State the conditions (there are more than...Ch. 4 - Prob. 4.6WPCh. 4 - W4.7 What is the difference between the stream...Ch. 4 - Under what conditions do both the stream function...Ch. 4 - Prob. 4.9WPCh. 4 - Consider an irrotational, incompressible,...Ch. 4 - Prob. 4.1FEEPCh. 4 - Prob. 4.2FEEPCh. 4 - Prob. 4.3FEEPCh. 4 - Given the steady, incompressible velocity...Ch. 4 - Prob. 4.5FEEPCh. 4 - Prob. 4.6FEEPCh. 4 - C4.1 In a certain medical application, water at...Ch. 4 - Prob. 4.2CP
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 viscous liquid of constant ρ and μ falls due to gravitybetween two plates a distance 2 h apart, as in Fig. P4.37. Thefl ow is fully developed, with a single velocity component w = w ( x ). There are no applied pressure gradients, onlygravity. Solve the Navier-Stokes equation for the velocityprofi le between the plates.arrow_forwardA two-dimensional, incompressible, frictionless fluid isguided by wedge-shaped walls into a small slot at theorigin, as in Fig. P4.52. The width into the paper is b , and the volume flow rate is Q . At any given distance r fromthe slot, the flow is radial inward, with constant velocity.Find an expression for the polar coordinate stream functionof this flow.arrow_forwardThe viscous oil in Fig. P4.88 is set into steady motion by aconcentric inner cylinder moving axially at velocity Uinside a fixed outer cylinder. Assuming constant pressureand density and purely axial fluid motion, solve Eqs. for the fluid velocity distribution υ z ( r ). What are theproper boundary conditions?arrow_forward
- Incompressible steady fl ow in the inlet between parallelplates in Fig. P3.17 is uniform, u = U 0 = 8 cm/s, whiledownstream the fl ow develops into the parabolic laminar profile u = az ( z 0 - z ), where a is a constant. If z 0 = 4 cm and thefl uid is SAE 30 oil at 20 ° C, what is the value of u max in cm/s?arrow_forwardOil, of density ρ and viscosity μ , drains steadily down theside of a vertical plate, as in Fig. P4.80. After a developmentregion near the top of the plate, the oil fi lm willbecome independent of z and of constant thickness δ .Assume that w = w ( x ) only and that the atmosphere offersno shear resistance to the surface of the fi lm. ( a ) Solve theNavier-Stokes equation for w ( x ), and sketch its approximateshape. ( b ) Suppose that fi lm thickness δ and the slopeof the velocity profi le at the wall [ ∂ w /∂ x ] wall are measuredwith a laser-Doppler anemometer (Chap. 6). Find anexpression for oil viscosity μ as a function of ( ρ , δ , g ,[ ∂ w / ∂ x ] wall ).arrow_forwardQ3) In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig.3 contains 12064 holes of 5 mm diameter. The suction velocity through each hole is Vs = 8 m/s, and the test section entrance velocity is V₁ = 35 m/s. Assume incompressible steady flow of air at 20°C, compute, Vo, V₂ and Vf in m/s. Test section D₁ = 0.8 m Uniform suction D₁= 2.2 m Do = 2.5 m V₂ -L=4 m Fig.3 L Vo-arrow_forward
- A fl uid jet of diameter D 1 enters a cascade of movingblades at absolute velocity V 1 and angle β 1 , and it leaves atabsolute velocity V 2 and angle β 2 , as in Fig. P3.78. Theblades move at velocity u . Derive a formula for the powerP delivered to the blades as a function of these parameters.arrow_forwardA solid circular cylinder of radius R rotates at angularvelocity V in a viscous incompressible fluid that is at restfar from the cylinder, as in Fig. P4.82. Make simplifyingassumptions and derive the governing differential equationand boundary conditions for the velocity field υ θ in thefluid. Do not solve unless you are obsessed with this problem.What is the steady-state flow field for this problem?arrow_forwardP3.51 When a jet strikes an inclined fixed plate, as in Fig. P3.51, it breaks into two jets at 2 and 3 of equal velocity V = Vjet but unequal fluxes aQ at 2 and (1 - a)Q at section 3, a being a fraction. The reason is that for frictionless flow the fluid can exert no tangen- tial force F, on the plate. The condition F, us to solve for a. Perform this analysis, and find a as a function of the plate angle 0. Why doesn't the answer depend on the properties of the jet? 0 enables aQ, V (2 P. Q, A, V (1) Fn F, = 0 (1-a) Q, V 3. P3.51arrow_forward
- A bellows may be modeled as a deforming wedge-shapedvolume as in Fig. P3.31. The check valve on the left(pleated) end is closed during the stroke. If b is the bellowswidth into the paper, derive an expression for outlet massfl ow m 0 as a function of stroke θ ( t ).arrow_forwardA belt moves upward at velocity V, dragging a fi lm ofviscous liquid of thickness h , as in Fig. . Near the belt,the fi lm moves upward due to no slip. At its outer edge, thefi lm moves downward due to gravity. Assuming thatthe only nonzero velocity is υ ( x ), with zero shear stress atthe outer fi lm edge, derive a formula for ( a ) υ ( x ), ( b ) the average velocity V avg in the fi lm, and ( c ) the velocity V c forwhich there is no net flow either up or down. ( d ) Sketchυ ( x ) for case ( c ).arrow_forwardExample (3.2) A fluid (p = steadily through tube. The section diameters are d, = 100mm and d,= 80 mm. The gauge pressure at 1 is p, =200 kPa. The velocity at 1 is u,= 5 m/s. The tube is horizontal (z=z,). What is the gauge pressure at 960 kg/m³) is flowing %3D %3D section 2?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
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License