Page 435 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 415

a) If the systolic pressure at the aorta is 120mmHg, what is the pressure in the
neck 25cm higher and at a position in the legs 90cm lower? The density of blood
is 1.05g/cm3.
b) The lowest point on the earth's surface is located in the western Pacific Ocean,
in the Marianas Trench. It is about 11 km below sea level. Estimate the pressure
at the bottom of the ocean. Take the density of seawater as 1025kg/m3.
c) The highest point on the earth's surface is the top of Mount Everest, located
in the Himalayas on the border of Nepal and China. It is approximately 8900m
above sea level. If the average rate of decrease in air temperature with altitude is
6.5 "C/ km, estimate the air pressure at the top of Mount Everest. Assume that the
temperature at sea level is 15 "C. Why is it difficult to breathe at high altitudes?
(Answer: a) Pneck = 100.7mmHg, qeg = 189.5mmHg b) 1090 atm c) 0.31 atm)

9.2 Oil spills on water can be removed by lowering a moving belt of width W
into the water. The belt moves upward and skims the oil into a reservoir aboard
the ship as shown in the figure below.

a) Show that the velocity profile and the volumetric flow rate are given by

Wpg63 cos p
&= - WV6
3P
b) Determine the belt speed that will give a zero volumetric flow rate and specify
the design criteria for positive and negative flow rates.

9.3 When the ratio of the radius of the inner pipe to that of the outer pipe
is close to unity, a concentric annulus may be considered to be a thin plate slit
and its curvature can be neglected. Use this approximation and show that the