FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Textbook Question
Chapter 4, Problem 18P
A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane:
u= 185+2.05x+0.656y
v = 0.754 -2.18x-2.05y
Calculate the acceleration field (find expressions for acceleration components axand ay). and calculate the acceleration at the point (x.y) = (-1.3).
Answers: ax=1.51, ay=2.74
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a. Derive an equation for the material acceleration vector.b. Obtain the vorticity vector for the velocity field.c. Is the flow rotational or irrotational? Show through your derivation.d. Is the flow incompressible or compressible? Show through your derivation.
1) A steady, incompressible, two-dimensional velocity field is given by the following
components in the xy-plane:
V(u, v) = (0.25 +1.4x + 0.8y)i + (-0.5 +0.9x - 1.4y)]
where the x- and y-coordinates are in m and the magnitude of velocity is in m/s.
a) Calculate the acceleration field (find expressions for acceleration components ax and ay)
b) Calculate the acceleration at the point (x, y) = (2, 3).
A velocity field of the two-dimensional, time-dependent fluid flow is given by
where t is time.
Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any
time t > 0 and any pont x > 0, y > 0.
a) Incompressibility
a) Is this flow incompressible (i.e. it has zero divergence)?
Yes
No
ди
Ət
b) Time derivative of flow field
Calculate the time derivative of the velocity. Represent your answer in the form
i+
||
3
3
u(t, x, y) =r? (x² + y² ) i− {etxtyj
X уј
3
a =
c) Material derivative and acceleration
Calculate the material derivative of the velocity and hence the acceleration a. Represent
your answer in the form
Du
Dt
||
j
i+
j
Chapter 4 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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