PROBLEM 1 (30 points)
Consider a Boeing 747-400 at weight close to the maximum takeo? weight (MTOW) cruising at
Mach 0.82 at an altitude of 32000 ft.
(a) How much thrust is needed to maintain cruise? Express your answer in kN and as a fraction of
the weight.
(b) What is the diameter of a sphere that would have the same drag as the Boeing 747-400 at the
same cruise conditions? How does the sphere diameter compare to the wing span of the 747?
PROBLEM 2 (30 points)
D
Shear stress t
Blood cells sustain serious damage (hemolysis) when they are subjected to shear stress exceeding
150 Pa. During blood transfusion, blood ?ows through a syringe needle with typical inner diameter
D= 0.603 mm. See chart at http//en.wikipedia.org/wiki/Needle_gauge_comparison_chart.
It’s the 20-gauge needle). The intent is to transfuse blood as quickly as possible without damaging
the cells.
The ?ow ?eld inside the syringe needle is well approximated by Poiseuille’s law (you can look it up
in the book), which can be worked out to give the following relation between the volume ?ow rate
Q and the wall shear stress t (the wall stress is the maximum stress):
Q =
1
32
pD3
µ
t
Here µ is the viscosity of the blood. Your task is to recommend to the administering doctor the
maximum permissible blood ?ow rate. Do your calculations in SI units, then convert your ?nal
answer to L/min (liters per minute, a unit that doctors understand...).
For the average human, how long will it take to replace their entire blood volume?
1