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W V UNIVERSITY Murdoch Examinations  Semester 1, 2009 €. Unit EXM224 PRINCIPLES OF UNIT OPERATIONS Exam Type : Internal & External Reading time : 10 minutes (Note taking allowed onto Exam Paper ONLY)
Exam Duration : 3 hours INSTRQQTIQNS This paper contains 3 pages and 5 questions. Spend 3035 minutes on each question. All questions are of equal value with respect to marks. Attempt all questions and answer in the answer booklet provided. 0 Marks will be allocated for stating relevant equations, assumptions and units in your
calculations. EXAMINATI ID L WED
CLOSED BOOK EXAM ANSWER BOOKLET Provided by the gandidgte
CALCULATOR (NO QWERTY KEYBOARD) Question 1 A ventun' meter is used to measure the ﬂow rate of an incompressible ﬂuid. ii
a 2 2
. . v v
Bernoulli equation 3‘ + Z1 + 4 = —p—2~ + 22 + —2— r 2g 7 2g 1(a) Use the equation of continuity to derive the relationship between velocities v1 and V2 at
points 1 and 2 in which the crosssectional area at point 1 is four times that at point 2. [4 marks]
1(b) Use the Bernoulli equation for the system to prove that
__ 15 p Q2
p] p 2 2 A12
[6 marks] 1(c) Suppose this meter is used to measure the ﬂow rate of a stream of water, using mercury
(SG = 13.6) as the manometer ﬂuid. Calculate the pressure drop plpz which satisﬁes a
manometer reading h = 52 cm. [5 marks] 1(d) Calculate the volumetric ﬂow rate. Pipe diameter at point 1 is 20 cm and the discharge
coefﬁcient is 0.96. [3 marks]
1(e) What are the disadvantages of a venturi meter ?
[2 marks]
Question 2
2(a) Brieﬂy discuss how you would obtain the friction factor for a
(i) ﬂuid ﬂow through a pipe,
(ii) particle settling in a ﬂuid.
[4 marks]
2(b) Brieﬂy explain the behaviour of a Newtonian nonsettling slurry.
[2 marks]
2(c) A slurry has 50% solids by mass of clay particles (SG of clay = 2.65).
Calculate
(i) the solids concentration in % solids by volume in the slurry, and
[2 marks] (ii) the slurry viscosity (viscosity of water = 0.001 N s m'z).
[2 marks] 2(d) The slurry described in part 2(e) is pumped through a horizontal 5 cm diameter,
smooth pipe. The average velocity of ﬂow is 5 cm s". Calculate the rate at which solids are transported (t h").
[3 marks] 2(e) Verify laminar conditions for the slurry ﬂow described in parts 2(c) and 2(d) and calculate the head loss per unit length of pipe.
[7 marks] Assume that the head loss in a smooth pipe carrying a Newtonian ﬂuid under laminar ﬂow
conditions may be calculated using the HagenPoiseuille equation: hf =32uLv p g D2
and the slurry viscosity is given by Ei=1+2.scv+locv2
no where CV is the volume fraction of solids and no = viscosity of ﬂuid. gum; 3(a) (i) Calculate the mass ﬂow rate of air (t h") required to dead roast a sulphide
containing 80% F632 and 20% SiOz to produce Fe203 and $02 at 550°C in a ﬂuid bed roaster.
Solid feed rate = 80 t/day
Air (21% 02, 79% N2) input = 110% of theoretical air (Fe =56, S=32, O = 16, N = 14)
[10 marks] (ii) Calculate the vol% composition of the exit gas from the roaster.
[5 marks] 3(b) A slurry (A) containing 40% solids by mass is fed into a solid/liquid separation unit at
a slurry feed rate of 150 t h". The two output streams (B and C) from the solid/liquid
separation unit contain pure water (B) and ﬁlter cake (C) containing 20% water by
mass. Sketch a block diagram to show the ﬂow of A, B and C and calculate the weight ﬂow rates of the two output streams B and C.
[5 marks] Question 4 Gold in the form of the aurocyanide ion is adsorbed from leach solutions onto activated
carbon granules. A stirred tank containing 100 m3 of solution containing 1 ppm gold is
treated with 1 kg of suspended carbon granules which can be assumed to be spherical with
diameter 1 mm. The mass transfer correlation for mass transport to suspended particles is
given by Sh = 2.0 + 0.6 or“ .Sc"3 = de/D where Gr = d3.(ps  pL) .g/(pL.v2), Sc = v/D and d is the particle diameter, g = 980 cm 3'2 is the acceleration due to gravi ,
ty 2 D = 1 x 10‘5 cm s'1 is the difﬁlsion coefﬁcient of aurocyanide ions, pg = 2.0 g cm‘3 is the
density of the carbon granules and m, =1.0 g cm'3 is the density of the solution, v = 0.01 cm 4(a) 4(b) 4(0) 4(d) 2 s'1 is the kinematic viscosity and k, is the mass transfer coefﬁcient. Calculate the mass transfer coefﬁcient to the carbon granules in cm s".
[6 marks] Assuming that the rate of adsorption of gold is controlled by mass transport of
aurocyanide ions to the surface of the granules, calculate the initial rate of gold adsorption in terms of Au mg min"l . [9 marks] Without making any additional calculations, sketch the shape of the curve that could
be expected for the concentration of gold in the solution in the reactor as a ﬁlnction of
time after adding the carbon. What assumption have you made? [3 marks]
Suggest two methods (with reasons) for improving the rate of adsorption of gold. [2 marks] Question 5 5(a) 5(1)) A wall of a furnace 0.244 m thick is constructed of material having a thermal
conductivity 1.30 W m'1 K". The wall will be insulated on the outside with material
having an average thermal conductivity 0.346 W m'1 K", so the heat loss from the
furnace will be equal to or less than 1830 W m'z. The inner and outer surface
temperatures are 1315 °C and 26 °C respectively. Calculate the thickness of insulation
required. AT 21%)
[10 marks] A small oxidized horizontal metal tube with an outside diameter 25 mm, length 60 cm
and surface temperature 315 °C is in a very large furnace enclosure with ﬁrebrick
walls surrounding air at 815 °C. Calculate the total heat transfer to the tube by
convection and radiation. Emissivity of metal tube = 0.66 116 for horizontal cylinder = 1.32(AT/D)“4 ) (T1 /100)4 — (T2/100)4
(T1 ' T2) q: h, = s(5.676 [10 marks]
End of Question Paper a.
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