Download ME 750A: Spring 2005 HW Due on Wednesday, March 9

ME 750A: Spring 2005 HW Due on Wednesday, March 9
1. It has been suggested that the velocity field near the core of a tornado may be approximated
by V = – er (q/r) + e (K/r). Does this represent incompressible flow? Is this an irrotational
flow? [FM 5.16, 5.78]
2. An incompressible fluid of negligible viscosity is being pumped through two tiny holes at the
centers of two parallel discs into the narrow gap (= h) between the disks. The fluid has only a
radial velocity component. The pressure at the edge of the gap (at r = R) is 1 atm. For a total
flow-rate of Q m3/s, plot the variation in pressure (p) in the gap as a function of r. [FM 6.10]
R
r
h
p= 1 atm
Q m3/s
3. Consider the flow-field obtained by combining a doublet and a uniform flow in class.
Choosing an appropriate free stream velocity and a cylinder radius, plot the stream function and
potential function around the cylinder with “line-contours” using a software such as MATLAB
(available in most computers in our labs).
4. Consider a long section of a large pipe half buried into the ground. The radius of the pipe is 3
m. A wind of 100 km/hr is blowing perpendicular to the axis of the pipe, and the static pressure
and temperature of the air are 100 kPa and 290 K, respectively. Assuming a steady, inviscid, and
incompressible flow, estimate the force (per unit length) tending to lift the pipe off the ground.
[FM 6.66]
5. A flow field is represented by the stream function  = x2 – y2. Find the corresponding velocity
field (express the vector V, or its components u and v, as a function of x & y). Show that this
flow field is irrotational and obtain the corresponding potential function. [FM 6.83]