Question

Question 03 (25 marks) A rotodynamic machine's shaft power (P) and pressure rise (Ps) on the volume flow rate (Q), diameter of the rotor (D), rotating speed (N), density of the liquid (p) and the dynamic viscosity (u) of the liquid. Obtain the corresponding dimensionless groups. I. across the unit depend (10 marks) SLIIT faculty of engineering expect to import wind tunnel setup that can deliver discharge of 4.8 m'/s with the total pressure rise of 75 mm water column and the shaft power of 3.1 kW at the installation. Before importing the wind tunnel, geometrically similar small model with 0.65 scale factor and having twice the rotational speed should be tested. If fully dynamic similarity achieved, determine the followings for the model if the air conditions are same in the both cases. II. (05 marks) a) Output discharge (05 marks) b) Pressure generated (05 marks) Shaft power required c)

Answer 1

1 given at Shaft PouleY (P) depends flowYale (a) diamelen of Yotan (d) Totaling sPeed (N) density of liuid () dynamic visconty () fnQ,d, N P - dependent Vaniable Independent Vaniable Total noofVaniables (n)= Repeating Variables (m) fluid/ dynami frpenty Fundametal urit kinemahic PYopenty moof dimension less terms 6-3 3" T-tenms Posrible PaTameten dimensional fomula M P -3 MLTO ML T MLT d

a b a, +3b,- +2 o 8-2 -'9- = O 3+ b 3-1-b a 3 -2 d P Pd b. a1 d o a,+3b b, = -I o a - 3 a a d uN d'Q 3 a, C d Q - bi La-b-+0 O

d'a J= Qd Pd3 sQd given data 4.8 m/s dischange () of wind tunneL; Protobpe totalpressure() to wwSL Wakn shatt pow P) = 3-1Kw 9Yavity henfaie FYoude's Lau Windtunnd is erpenienced by applicable is L P = O.6S given, Scale factot 라구 model dischange a. v, veleciy vha Ar Vr 5/2 5la Lm Lp Qm 4.8 4.09 m/s Qm Model dischorg

enenated: PYessure a F A LY PP Lp Pm 1 O 6 S 15 mm af afe I5.38 4 shaft Pouun: C. Fr VY mar JLY Y2. 2 LY C LY PP 기2 Pm Vo.65) 3. 1 4.16 KW A