umn ME 3332 HW 9 info (Hogan) Spring 2011 - ME 3332 Spring...

ME 3332 Spring 2011
HW #9 A &B
Assigned- Monday, March 21st, 2011
Due- Monday, March 28th, 2011
Source Material: Class Notes, 6.1-6.4 “Fundamentals of Fluid Mechanics” by
Munson, Young, & Okiishi (5th or 6th edition).
Please Show All Work and Follow the Format given on the course website for
Type B Problems
Type A.
Section 6.1 of “Fundamentals of Fluid Mechanics” by Munson, Young, &
Okiishi (5th or 6th edition).
1. A fluid has a velocity field given as: V = 2x
2
i – (2xy - 2yz) j – (2xz + z
2
) k . What
is the volumetric dilatation rate of this fluid?
2. Consider the same velocity field as problem 1. Calculate the vorticity, z. Is the
flow irrotational?
Section 6.2 of “Fundamentals of Fluid Mechanics” by Munson, Young, &
Okiishi (5th or 6th edition).
3. The velocity field for a certain incompressible, steady flow field is V = (x
2
+y
2
) i
–(xy+yz+z) j + (g[x,y,z]) k . Determine possible functional form for g [x,y,z].
4. The velocity field for a 2-dimensional incompressible flow, is given as V =
(3yt)i + (4xt)j . Find the stream function of this flow.