Civil Engineering Reference
In-Depth Information
PROBLEMS
8.1
Per the standard definition of viscosity described in Section 8.1, how would you
describe the property of viscosity, physically, in terms of an everyday example
(do not use water and molasses—I already used that example)?
8.2
How would you design an experiment to determine the
relative
viscosity
between two fluids? What fluids might you use in this test?
8.3
Look into a fluid mechanics text or reference topic. What is the definition of a
Newtonian fluid
?
8.4
Equation 8.5 is a rather complicated partial differential equation, what does
it really mean? Explain how that equation takes the very simple form of
Equation 8.6.
8.5
If you visually examine a fluid flow, could you determine whether it was
rotational or irrotational? Why? Why not?
8.6
Why do we use the Green-Gauss theorem in going from Equation 8.16 to
Equation 8.17? Refer to Chapter 5.
8.7
Recalling that Equation 8.21 is based on unit depth in a two-dimensional flow,
what do the nodal forces represent physically?
8.8
Given the three-node triangular element shown in Figure P8.8, compute the
nodal forces corresponding to the flow conditions shown, assuming unit depth
into the plane.
3
(0, 1)
2
U
(1, 0)
1 (0, 0)
Figure P8.8
8.9
Per Equation 8.32, how do the fluid
velocity
components vary within
a.
A linear, three-node triangular element.
b.
A four-node rectangular element.
c.
A six-node triangular element.
d.
An eight-node rectangular element.
e.
Given questions
a
-
d
, how would you decide which element to use in a finite
element analysis?
8.10
We show, in this chapter, that both stream function and velocity potential
methods are governed by Laplace's equation. Many other physical problems
are governed by this equation. Consult mathematical references and find
other applications of Laplace's equation. While you are at it (and learning
