Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259877827
Author: CENGEL
Publisher: MCG
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Chapter 9, Problem 75P
To determine
Whether the speed of flow in a particular region of the flow is relatively small or large.
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The locus of fluid particles that have passed sequentially through a prescribed point in the flow is called a (a) Pathline (b) Streamtube (c) Streamline (d ) Streakline (e) Timeline
Contrast the governing physical assumptions that are made in analysing flow
under models of both ideal and real fluids. For what type of flow is the ideal
model a reasonable approximation. Using sketches in your answer, include an
illustrative example to show the differences that occur when applying these
models.
h
film
surface
air
X
By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane.
expressions for velocity are:
v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cosθ
v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sinθ
Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dACh. 9 - Prob. 4CPCh. 9 - Prob. 5CPCh. 9 - Prob. 6CPCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P
Ch. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Alex is measuring the time-averaged velocity...Ch. 9 - Let vector c be given G=4xziy2i+yzkand let V be...Ch. 9 - The product rule can be applied to the divergence...Ch. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20CPCh. 9 - In this chapter we derive the continuity equation...Ch. 9 - Repeat Example 9-1(gas compressed in a cylinder by...Ch. 9 - Consider the steady, two-dimensional velocity...Ch. 9 - The compressible from of the continuity equation...Ch. 9 - In Example 9-6 we derive the equation for...Ch. 9 - Consider a spiraling line vortex/sink flow in the...Ch. 9 - Verify that the steady; two-dimensional,...Ch. 9 - Consider steady flow of water through an...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Two velocity components of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - What is significant about curves of constant...Ch. 9 - In CFD lingo, the stream function is often called...Ch. 9 - Prob. 39CPCh. 9 - Prob. 40CPCh. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - As a follow-up to Prob. 9-45, calculate the volume...Ch. 9 - Consider the Couette flow of Fig.9-45. For the...Ch. 9 - Prob. 48PCh. 9 - AS a follow-up to Prob. 9-48, calculate the volume...Ch. 9 - Consider the channel flow of Fig. 9-45. The fluid...Ch. 9 - In the field of air pollution control, one often...Ch. 9 - Suppose the suction applied to the sampling...Ch. 9 - Prob. 53PCh. 9 - Flow separates at a shap corner along a wall and...Ch. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 58PCh. 9 - Prob. 59PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63EPCh. 9 - Prob. 64PCh. 9 - Prob. 65EPCh. 9 - Prob. 66PCh. 9 - Prob. 68EPCh. 9 - Prob. 69PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Wht in the main distionction between Newtormine...Ch. 9 - Prob. 77CPCh. 9 - What are constitutive equations, and to the fluid...Ch. 9 - An airplane flies at constant velocity Vairplane...Ch. 9 - Define or describe each type of fluid: (a)...Ch. 9 - The general cool volume from of linearmomentum...Ch. 9 - Consider the steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider liquid in a cylindrical tank. Both the...Ch. 9 - Engine oil at T=60C is forced to flow between two...Ch. 9 - Consider steady, two-dimensional, incompressible...Ch. 9 - Consider steady, incompressible, parallel, laminar...Ch. 9 - Prob. 89PCh. 9 - Prob. 90PCh. 9 - Prob. 91PCh. 9 - The first viscous terms in -comonent of the...Ch. 9 - An incompressible Newtonian liquid is confined...Ch. 9 - Prob. 94PCh. 9 - Prob. 95PCh. 9 - Prob. 96PCh. 9 - Prob. 97PCh. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Consider again the pipe annulus sketched in Fig...Ch. 9 - Repeat Prob. 9-99 except swap the stationary and...Ch. 9 - Consider a modified form of Couette flow in which...Ch. 9 - Consider dimensionless velocity distribution in...Ch. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Prob. 104PCh. 9 - Prob. 105PCh. 9 - Prob. 106PCh. 9 - Prob. 107CPCh. 9 - Prob. 108CPCh. 9 - Discuss the relationship between volumetric strain...Ch. 9 - Prob. 110CPCh. 9 - Prob. 111CPCh. 9 - Prob. 112PCh. 9 - Prob. 113PCh. 9 - Look up the definition of Poisson’s equation in...Ch. 9 - Prob. 115PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - For each of the listed equation, write down the...Ch. 9 - Prob. 119PCh. 9 - Prob. 120PCh. 9 - A block slides down along, straight inclined wall...Ch. 9 - Water flows down a long, straight, inclined pipe...Ch. 9 - Prob. 124PCh. 9 - Prob. 125PCh. 9 - Prob. 126PCh. 9 - Prob. 128PCh. 9 - The Navier-Stokes equation is also known as (a)...Ch. 9 - Which choice is not correct regarding the...Ch. 9 - In thud flow analyses, which boundary condition...Ch. 9 - Which choice is the genera1 differential equation...Ch. 9 - Which choice is the differential , incompressible,...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady velocity field is given by...Ch. 9 - Prob. 137P
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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
- V u-v Question 4: Consider fully developed Couette flow - flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary as illustrated. The flow is steady, incompressible, and two dimensional in the xy-plane. The velocity field is given by V = (u,v) = (V y/h)ỉ + 0ỷ, Generate an expression for stream function Yalong the vertical dashed line in the figure. For convenience, 4= 0 along the bottom wall of the channel. What is the value of Y along the top wall?arrow_forwardThe actual path traveled by an individual fluid particle over some period is called a (a) Pathline (b) Streamtube (c) Streamline (d ) Streakline (e) Timelinearrow_forwardFlow separation: Using sketch, briefly describe the phenomena of flow separation at an arterial bifurcation region; Explain the possible factors which may influence flow separation of this kind. If you select a line which is perpendicular to the main flow and passing the main flow region and the separated region, draw the possible velocity profile along that line.arrow_forward
- Oil relation between the shear stress and rate of deformation is given in the figure, If the oil density is =270.5 kg/m what is its viscosity in (m /s)? Oil 20 Rate of deformation, duldy Lenovo K9 Note Al Dual Camera Shear stress, 7arrow_forwardA steady, incompressible, two-dimensional CFD calculation of flow through an asymmetric two-dimensional branching duct reveals the streamline pattern sketched in Fig, where the values of ? are in units of m2/s, and W is the width of the duct into the page. The values of stream function ? on the duct walls are shown. What percentage of the flow goes through the upper branch of the duct?arrow_forwardConsider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary as illustrated in figure below. The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity field is given by: V = (u, v) = V +07 h Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the z- direction. Do fluid particles in this flow rotate clockwise or counterclockwise? u = varrow_forward
- Define vorticity in terms of the vector velocity field. How is the “rotation” of a fluid particle related to its vorticity? In Cartesian coordinates, write down the general form of the z-component of vorticity. What is the condition on the vector velocity field such that a flow is irrotational?arrow_forwardFor each statement, choose whether the statement is true or false, and discuss your answer briefly. (a) The velocity potential function can be defined for threedimensional flows. (b) The vorticity must be zero in order for the stream function to be defined. (c) The vorticity must be zero in order for the velocity potential function to be defined. (d) The stream function can be defined only for two-dimensional flow fields.arrow_forwardA curve that is everywhere tangent to the instantaneous local velocity vector is called a (a) Pathline (b) Streamtube (c) Streamline (d ) Streakline (e) Timelinearrow_forward
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