PROBLEMS
1. Show that the
following heat transfer equation is consistent in its units:
q = UADT
where q is the
heat flow rate (J s-1), U is the overall heat transfer
coefficient (J m-2 s-1 °C-1), A
is the area (m2) and DT
is the temperature difference (°C).
2. The specific heat of apples is given as 0.86 Btu lb-1 °F-1.
Calculate this in J kg-1 °C-1.
(3600 J kg-1 °C-1 = 3.6
kJ kg-1 °C-1)
3. If the viscosity of olive oil is given as 5.6 x 10-2 Ib ft-1
sec-1, calculate the viscosity in SI units.
(83 x 10-3 kg-1m-1
s-1 = 83 x 10-3 N s m-2)
4. The Reynolds number for a fluid in a pipe is
 |
Dvr
|
|
|
|
µ
|
where D is the diameter of a pipe, v is the velocity of
the fluid, r
is the density of the fluid and µ
is the viscosity of the fluid. Using the five fundamental dimensions [M],
[L], [T], [F] and [t] show that this is a dimensionless ratio.
5. Determine the protein content of the following mixture, clearly showing
the accuracy:
|
|
|
|
%
Protein
|
Weight
in mixture
|
|
|
|
| Maize
starch |
0.3
|
100
kg
|
| Wheat
flour |
12.0
|
22.5
kg
|
| Skim
milk powder |
30.0
|
4.31
kg
|
|
|
|
(3.4%)
6. In determining the average rate of heating of a tank of 20% sugar syrup,
the temperature at the beginning was 20°C and it took 30 min to heat
to 80°C. The volume of the sugar syrup was 50 ft3 and its
density 66.9 lb/ft3. The specific heat of the sugar syrup is
0.9 Btu lb-1°F-1.
(a) Convert the specific heat to kJ kg-1 °C-1.
(3.8 kJ kg-1 °C-1)
(b) Determine the rate of heating, that is the heat energy transferred
in unit time, in SI units (kJ s-1).
(191.9 kJ s-1)
7. The gas equation is PV = nRT.
If P the pressure is 2.0 atm, V the volume of the gas is
6 m3, R the gas constant is 0.08206 m3 atm
mole-1 K-1 and T is 300 degrees Kelvin, what
are the units of n and what is its numerical value?
(0.49 moles)
8. The gas law constant R is given as 0.08206 m3 atm
mole-1 K-1.
Find its value in:
(a) ft3 mm Hg Ib-mole-1 K-1,
(999 ft3
mm Hg Ib-mole-1 K-1)
(b) m3 Pa mole-1 K-1,
(8313 m3 Pa mole-1 K-1)
(c) Joules g-mole-1 K-1.
(8.313 x 103 J g-mole-1 K-1)
Assume 1 atm = 760 mm Hg = 1.013 x 105 N m-2. Remember
1 Joule = 1 N m, and in this book mole is kg mole.
9. The equation determining the liquid pressure in a tank is z = P/rg
where z is the depth, P is the pressure, r
is the density and g is the acceleration due to gravity. Show that
the two sides of the equation are dimensionally the same.
10. The dimensionless Grashof number (Gr) arises in the study of natural
convection heat flow. If the number is given as
|
D3r2bgDT
|
|
|
|
µ2
|
verify the dimensions of b
the coefficient of expansion of the fluid. The symbols are all defined in
Appendix 1.
([T]-1)
 CHAPTER
2: MATERIAL AND ENERGY BALANCES
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