Question

11. To learn the power required to overcome drag. a II-group: P/(PAV) where the variables are power, density, area and velocity, is used. In an experiment, with a 1/8" scale model, the power loss was measured at 5 when the air velocity was 0.5 m/s. a. Verify the pi group is dimensionless. b. Calculate the power lost in the protatype when the air velocity is 4 m/s. The density of air in both cases is 1.22 kg/m a 12. A water jet (p=1000kg /m") is deflected by a vane as shown in the image below. The incoming jet has a speed of 30 m/s and a diameter of 25 cm. Find the force exerted by the jet on the vane. 60

Answer 1

The answers to all the subparts of the Question-11 is described in the images below:

(Q:-11) criven T-group : Page 1 P (SAV) Now, the dimensions of each variable of the T-group are: Р Power M' L 27-3 s Density M'L-3 A Area L2 velocity - LT-1 Now, implementing these dimensions of each variable in the given T-group, we have, T-group: P SAV? (M'2² T-3) (M' L-3). (L²) CL'T13 M'L²T-3 M' L² T 3 - group = MOLOTO * Dimensionless. Verified Now, given oth scale model scale ratio, Le = 8 = Lp be = de Im dm Where L, b anda refers to length, width and diameter respectively and 'p' stands for prototype and m for model!)

Page 2 . Area of Prototype (Ap) Area of model (Am) Lp x be Lmx bm Х (1) Lm Les x lą (8)² =64 2 Am Now, Power loss for model, Pm=5w Air-velocity for model, um = 0.5 m/s Air- velocity for prototype, up = 4 m/s Density of air for both (model and prototype), sm sp = 1.22 kg/m3 from the relation, - SO Garam P Govo) SAV3 SAV² Pm Pp so Ap up 3 3 Pp Pm x х Ap Am 5 X 64 X(4 3 0.5 163840 W = 163.840 KW Prototype -Ans