H1029 ENGINEERING FLUID MECHANICS 2.a) Briefly describe the following A. Geometr
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Question
H1029 ENGINEERING FLUID MECHANICS 2.a) Briefly describe the following A. Geometric similarity B. Kinematic similarity [6 marks] b) The aerodynamic testing of a drone aircraft flying at a speed of 540 km/hr is to be conducted. The testing is carried out in a water tunnel where a fixed velocity of 10 m/s is to be used. Calculate the scaling (full scale to model) required for the model aircraft to ensure dynamic similarity. (Par-1.2 kg/m3, pwater = 103 kg/m3·lair = 1.8 x 10-5 kg/ms, lwater-10-3 kg/ms). Since only low-speed aerodynamic testing is intended, neglect the Mach number effects. 540 km/hr [10 marks)] c) In the above example if a wind tunnel with a fixed air speed of 75 m/s is used instead of the water tunnel what will be the scaling requirement? [4 marks]Explanation / Answer
2.(a) Answer:
(i) Geometric Similarity:
The ratio of all corresponding linear dimension in the model and prototype are equal.
Here
Model is the small scale replica of the actual structure or machine. It is not necessary that models should be smaller than the prototypes (although in most of the cases it is), they may be larger than the prototypes.
and Prototype is the actual structure or machine.
Let Lm = length of model
bm = width of model
dm = diameter of model
Am = Area of model
Vm = Volume of model
and Lp, bp, dp, Ap, Vp are corresponding values of the prototype.
Lp/Lm = bp/bm = dp/dm = Lr
Ap/Am = Lr2 and Vp/Vm = Lr3
(ii) Kinematic Similarity:
Means the similarity of motion between model and prototype. Thus kinematic similarity is said to exist between the model and the prototype if the ratios of the velocity and acceleration at the corresponding points in the model and prototype are the same in magnitude; the directions also should be parallel.
Vp1/Vm1 = Vp2/Vm2 = Vr and
ap1/am1 = ap2/am2 = ar.
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