Question

A medium-size centrifugal air compressor has 32 radial blades and the inlet vanes allow air suction with no pre. whirl. The rotor speed is 7800 rpm and the tip radius is r2 = 0.25 m. Air is sucked in at a static temperature T1 = 305 K with an absolute velocity V1 = 80 m/s and a mass flow rate of 1.65 kg/s. The total-to total efficiency of the compressor is 80% and the power input factor is w = 1.02. Assume k = 1.4, Cp = 1.005 kg/kJ.K. Find the following quantities. a. The stagnation temperature at the impeller inlet To1 K b. The power input to the compressor = kW c. The total pressure ratio .

Answer 1

+ Soletion - medium - size centrifugal air compressor → Mo, of blades z = 32 N = 7800 rpm - No poc whire Tip Radius r₂ = 0,25m - stutic temperature ineet T=305k → absolute velocity wi=go mis muss How Rete m = 1.65 kg 75 - comp, = so o% power inpur Factor 4 =1.02 k=r=104 and co= 1.005 kJ / kg.k → stagnation temp. aut inlet To= ,+ = 305 + 3 x 180) 1005 CP

Toi = 308.18k un → As we know For centrifugal air comp. with inet condition of no pac whire Power input to comp. is w = e.eloupe mu 4 = input power Factor = 1.02 es= slip factor 42 = tip velocity of (blade) = TDaN 60 4= TX (0,5)*780° = 204,2035 mm3) 60 → for en let us stenitz corelation for Centrifugal impenes slip factor u = 1 - 0.63 T z u= 1- 0.63 T = 0.93814 m m 32 - using equation @ ® and w = 1.02 X 0.93814 X (204.2035) ..W=39.9019 kW mm 6) - And also for compressor w=cp ( Toz - Tom To2 = A crucel temp. of air after comps.

39.9019 = 1.005 * 1.65 (Toz' - 308.18) Toh = 332.24 un © Now For comp. n Required Theosticul m. Actuch required Toz - Toi 0.80 = To2 - Tol ... Toz = 327.43 k nr ② ہی وہ 1.4 l 0.4 - Poz ( 327.43 308.18 Pol = total = = 10 23 623 paessure Pol Retio.