1st HOMEWORK, Due Jan. 30th, 2022
A. Calculate pressure in the following cases of static equilibrium :
(a) In atmospheric air (assume ideal gas behavior) as a function of elevation z
measured in meters, if the temperature changes with elevation according
to 𝑇(𝑧) = (300 − 0.0065𝑧)𝐾. In addition, compute pressure at altitude z
= 2km.
(b) On the walls of a balloon containing 0.25kg of air at altitude z = 100m (use
the previous result for pressure and density). In addition, compute the
radius of the balloon.
(c) At the bottom of a cylindrical tank (open to the atmospheric air) of radius
R = 1m, containing 6.28 × 103kg water at 40C (give the result in psia units).
(d) Under the 36-in2 area of the shoe of a 170-lbm man.
(e) Under the 3-in2-area shoe of a hockey player of 170-lbm weight, on ice.
[8 points]
B. Calculate density in the following cases :
(a) Air (ideal gas) at temperature 00C and pressure 2 atm
(b) Helium (ideal gas) that fills a 10-m3 volume at temperature 250C, whose
gauge pressure reads 1.5 atm
(c) Granular iron of spherical grains of average diameter D = 1mm packed in a
1-grain/mm3 arrangement (density of iron  = 9g/cm3). Assume that the
void in each mm3 is filled with air. Discuss why the result is expected. Make
the same computation if the average diameter of the spherical grains are D
= 0.25 mm packed in a 64-grain/mm3 . Discuss why the result for the
density of both arrangements is the same.
[8 points]
C. Consider the situation in Fig. 1.8 [p. 14] in the Textbook. Assume that there is
one fluid with viscosity 𝜇 under shear between the parallel plates. Assume,
also, that two different forces 𝐹1 , 𝐹2 are applied to the upper moving plate. Use
the equations 1.12, 1.13 and 1.14 [p. 14] in the Textbook to derive a relation
between the ratio of the velocities and the forces of the moving plate . Describe
the result with words (one sentence is enough). Does this result make sense?
Draw a sketch of the velocity distributions to justify your judgement.
[10 points]
D. Solve problems 1 to 4 from the Textbook (p. 42)
[10 points]
E. Solve problem 34 from the Textbook (p. 52). Use commercial software (like
Excel) or trial and error or Newton Raphson to answer part (b). Since the void
fraction  obtains values between 0 and 1, a good initial guess is within this
range of numbers (0 <  < 1).
[10 points]
Total number of points 46