Chemical Engineering 140 August 31, 2015
Problem Set #2
(Due Wednesday, September 9)
7. 2.34 also answer part (c)
(c) What is the reaction-rate expression in a batch stirred tank reactor?
8. Given on a previous midterm
An incompressible, nonvolatile liquid is pumped into the bottom of a closed
tank of volume Vo and diameter D. At the start of filling, the tank contains only
an inert, ideal gas, such as air, that is insoluble in the liquid. The initial pressure
in the tank is po, and the supply liquid volumetric flow rate is proportional to the
difference in the inlet line pressure, pin and the pressure in the tank, p (which is
constant throughout the tank). The process is isothermal.
a. Draw a sketch of the filling process and describe in words what happens.
b. What is the final pressure in the tank?
c. Perform a mass balance on the gas phase to establish the transient pressure in
the tank as a function of the liquid volume.
d. What is the liquid height in the tank at the final pressure?
e. Perform a mass balance on the liquid to derive an implicit expression for the
liquid height in the tank as a function of time in terms of the parameters po, pin,
Vo, and D.
9. A spherical metal drum is slowly filled with benzene as shown in Figure 10.
a. Derive a mathematical formula for ρ, the density in kg/m3 of benzene-containing
drum as a function of the following:
h, the depth of benzene
R, the radius of the spherical tank
ρb, the density of benzene
md, the mass of the empty metal drum
b. If the diameter of the drum is 2.00 m, the density of the benzene is 0.879 g/cm3,
the mass of the empty metal drum is 200 kg, and h = 1.75R, will the drum float or
sink if sealed and placed in water? Show your work.
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