Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10P
To determine
Sketch of the profile of modified pressure and shading of the region of hydrostatic pressure.
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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 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 = v
Consider the pipe annulus sketched in fig. Assume that the pressure is constant everywhere (there is no forced pressure gradient driving the flow). However, let the inner cylinder be moving at steady velocity V to the right. The outer cylinder is stationary. (This is a kind of axisymmetric Couette flow.) Generate an expression for the x-component of velocity u as a function of r and the other parameters in the problem.
Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite
parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a
forced pressure gradient dP/dx driving the flow as
illustrated in the figure (dP/dx is constant and
negative). The flow is steady, incompressible, and
two-dimensional in the xy-plane. The velocity
components are given by
1 dP
u(y)
u =
2μ dx
(y²hy); v = 0
where is the fluid's viscosity. Is this flow rotational or irrotational?
a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this
flow rotate clockwise or counterclockwise?
b. calculate the linear strain rates in the x- and y-directions, and
c. calculate the shear strain rate ɛxy.
d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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- Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,arrow_forwardPerform the convective on velocity vectors u in cylindrical coordinates : Du/Dtarrow_forward1. A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). + b. Flow shear stress is governed by the following equation ôu Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in tems of the pressure gradient when the shear stress at the bottom plate is zero. Moving plate at Um/s N= N-1 `Fixed plate FIGURE Q1arrow_forward
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