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IIIIII Examination Paper SEMESTER: SECOND SEMESTER EXAMINATIONS 2008 UNIT: EN8201 FLUID MECHANICS  THEORY 1 DURATION OF EXAMINATION: PERUSAL: 10 MINUTES
WORKING: 2 HOURS EXAMINATION MATERIAL SUPPLIED BY THE UNIVERSITY: EXAMINATION BOOKLETS — TWO (2) PER STUDENT
GRAPH PAPER MM  TWO (2) PER STUDENT
EQUATION SHEETS  TWO (2) PAGES ATTACHED
CHARTS  TWO (2) PAGES ATTACHED EXAMINATION MATERIAL SUPPLIED BY THE STUDENT: WRITING IMPLEMENTS
CALCULATORS  ANY TYPE INSTRUCTIONS TO STUDENTS: Students are prohibited from having mobile phones or any other device capable of communicating information
(either verbal or written) in their possession during the examination NOTES MAY BE MADE ONLY ON THE EXAMINATION PAPER DURING PERUSAL TIME SEC  IONS A AND B  FIVE (5) QUESTIONS ONLY ARE TO BE ATTEMPTED ATTEMPT EACH SECTION IN A SEPARATE EXAMINATION BOOKLET ALL QUESTIONS ARE OF EQUAL VALUE Queensland University of Technology GUT GUT GUT Gardens Point Kelvin Grove Carseldine 1 SECTION A — attempt these questions in a separate booklet. QUESTION I. A shallow circular dish has a sharp edged oriﬁce at its centre, as illustrated in Figure Q1. A
water jet, with velocity V= 5m/s, strikes the dish concentrically. Determine the external
restraining force required to hold the dish in place if the jet issuing from the oriﬁce and dish also
have velocities V= 5m/s and there are no frictional losses as the water ﬂows over the surface of
the dish. The diameters of the water jet are D = I 00mm and d = 20mm, respectively. (Weighting 100%) V 9:45“
\ D
spherical dish
V water V
d
V /
Figure Q1. ENB201T1.082 cont/... QUESTION 2. An oriﬁce plate is to be used to measure the volume flow rate of air ﬂow through a duct 2.0m in
diameter, see Figure Q2. The mean velocity of air in the duct is not to exceed 20m/s and a water
tube manometer, having a maximum difference between water levels of 11 ﬂ 160mm, is to be
used to measure pressure drop. Assuming the coefﬁcient of discharge for the oriﬁce plate to be
0. 64, determine the oriﬁce diameter d to make full use of the manometer range. Take the density
of air to be 1.2kg/m3. (Weighting 100%) oriﬁce plate ‘ L?! ¢200mm mN duct
11 = 160mm water Figure Q2. ENB201T1.082 contl. .. QUESTION 3. The gate AB in Figure Q3 is 5m long, 2.4m Wide ( into the paper) and 25mm thick, made from
steel with a relative density of 7.85; it is hinged at B and rests against a stop atA. If the density of water is 990kg/m3 and a viscosity of 0. MIR: 3, determine the water level I: that wolud cause
gate to start falling. (Weighting 100%) frictionless pulley ENBZOIT1.082 contl. .. 4 SECTION B — attempt these questions in a separate booklet. QUESTION 4. A water network consists of two reservoirs, A and B, connected by a pipe system as shown in
Figure Q4. The pipe system consists of 500mm and 300mm diameter pipes and two 90” medium
roughness mitre bends. The entrance to the pipe system is ﬂush. Other properties of the pipes are
given in Figure Q4. Assuming that the density and kinematic viscosity of water are 1000kg/m3 and 1.1 x 10'6 m2/s,
respectively:
(a) Calculate the head delivered by the pump to achieve 1501/5 discharge.
(50% Weighting) (b) Draw total energy line indicating both frictional head loss and minor losses.
(30% Weighting) (0) If the efﬁciencies of the pump and electric motor used are 75% and 90%, respectively,
calculate the electric power required to drive the motor.
(20% Weighting) All relevant minor losses are to be considered in your calculations. Refer to the attachments for additional information. Figure Q4. ENBZOITIDSZ cont/... QUESTION 5. A city’s water network consists of three reservoirs; A, B and C, as shown in Figure Q5.
ReservoirA is large enough to be considered an unlimited pool of water, and both B and C are
small supply reservoirs which require a continuous supply from A. The free surface levels of
each reservoir are shown in Figure Q5 with respect to the Australia Height Datum (AHD). The
water demands from reservoirs B and C are 180175 and 1001/5, respectively. Pipe AB contains a
pump P, and pipe BC contains a valve X. Other details of the network are as shown in Figure Q5. (a) Calculate the discharge through pipe AC.
(30% Weighting) (b) Calculate the maximum ﬂow through pipe BC. Comment on the position of the valve X
(open, closed, partially open) such that pipe BC supplies the remainder of the demand in
reservoir C. (3 0% Weighting) (0) What should be the minimum head supplied by the pump P to satisfy the demands of
reservoirs B and C.
(40% Weighting) Minor losses may be neglected. Take the density and kinematic Viscosity of water to be 1000kg/m3 and 1.1 x 10'6 mz/s,
respectively. Refer to the attachments for additional information. 9(3) = 1801/3 Q(Q = 100% Figure Q5. ENB201T1.082 contl. .. QUESTION 6 Figure Q6 shows a test arrangement used to measure the lateral force that creates reverse—swing
on a cricket ball. A geometrically similar model cricket ball, with dimensions twice that of the
actual one, is used for the test. The model cricket ball has a diameter of 450mm and is ﬁxed at
the centre of a water ﬂume using the lever arrangement shown. The lever is hinged at the ﬂume
bed. Appropriate measuring devices are placed to measure longitudinal and lateral forces (F and
L) at the end of the lever arrangement. It may be assumed that the model cricket ball is adequately submerged to eliminate free surface
effects and the ﬂow in the ﬂume has uniform velocity proﬁle. (a) (b) (C) If the laboratory test is to replicate a cricket ball travelling at 140km/h through the air,
calculate the corresponding ﬂow velocity at the ﬂume. Densities and kinematic viscosities
of air and water are pa: 1.2kg/m3, v“ = 15 x 10'6 m2/s, pw = 998kg/m3 and vw = 1.2 x 10"
mz/s, respectively. (30% Weighting) Estimate the longitudinal force F that restrains the longitudinal movement of the model
cricket ball during the test. The lever is a 30mm diameter cylindrical rod with lengths as
shown in Figure Q6. The drag coefﬁcients CD for a sphere and cylindrical rod are 0.6 and 1.2 res ectivel .
P Y (40% Weighting) During the model test, the lateral force L is measured as 3N. Estimate the lateral force on the actual cricket ball that generates reverse swing.
(30% Weighting) Front Elevation Side Elevation Figure Q6. END OF PAPER ENBZOITIDSZ General data: Atmospheric Pressure:
Density of Water: Speciﬁc Gravity of Mercury:
Gravitational Constant: Viscosity: Compressibility: Fluid Under Gravity: Centre of Pressure: Metacentric Height and Radius: Continuity Equation: Mass Flow Rate: Momentum: Energy: Power: ENBZOIT1.082 (0 Equation Sheet 101.3kPa.
1000kg/m3.
13.6 9. 81m/s2. dv R=pgAJ7=rJ7A
BM=£
V
GM=£
W6 2F =n’z(v2 "vr) 2 2
£i+v—’+z,=&+12—+z2+w—q
pg 2:3: pg 2g P=ngH . DVp DV
Reynolds Number — Plpe ﬂow: R8 = T = 7
V
Froude Number F = _ _ . h _ L V2
DarcyWersbach Equatlon: f “ f 3%
I
Manning Equation: V = Flt—S ”2112/3
Hazen Williams Equation V = 0. 849C HWR0'63 SM“
1 2
Drag Force D = EPCDU A
F
Force Coefﬁcient Cf = I
_ V2 L2
2 P
AP
Pressure Coefﬁcient Cp 2 1
2
3 PV Properties of some areas: "In ENBZOITLOSZ (iii) , . V _, 7 «Ed 3523:."— E Q38... 35m .83.“: E 3&8 .3033 a xadwﬁogm=§ommm5©uctwmsgm ”=mE.o
x: .uwﬁonawciummﬂuig "0:32: ENB201T1.082 r . :5 9:55.. «01.: 5.39:0 2 oEuBEaa
amﬁhﬁﬁgwﬁﬁw :20 SEE 83
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RADIUS NOTES:
1 To obtain approximate head loss in metres multiply k by V2/2g (V = velocity in m/s, g = acceleration due to gravity in mfsz).
2 All valves fully open unless otherwise indicated.
See Appendix A, Example 3 for an example of calculations. 4 Brackets signify a range of values. CHART 14 RESISTANCE COEFFICIENTS OF VALVES AND FITTINGS Loss Coeﬂicients ENB201T1.082 ...
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