Question

Figure 5b. Open Cabriolet. Ca= 0.45 b). A pump in fig.6 is required to pump water at 60 L/s from point 1 to 2. The water is pumped using a 0.1 m diameter pipe. Taking the overall pump effi- ciency to be 70%, determine the power required by the pump and the pressure values at point Land M. Consider the density of water to be 1000 kg/m3 and express your answers for pressure in kN/m2. 4. a) A drag coefficient of 0.36 is produced by a fully closed Mercedes-Benz E-Class Cabriolet moving at speed of 65 km/h. On the other hand, when the win- dows and roof open is open Ca increases to 0.45. As- suming that the vehicle in both instances will need the same amount of power to overcome drag, find the speed that the open Cabriolet will need, when the frontal area remains the same. 0.1 m dia. M 4 m - Pump L SPA 905 4 m Figure 5a fully closed Cabriolet. Ca=0.36 Water sump Figure 6 [10+15=25 Marks] S.PA 4965

Answer 1

Bondary Layer ↑ TTTT TTTTT IZTI FITIMTITIE 122 X=0 tig (6) figla) Od 2=0.45 CDI = 0.36 Vi= 65km/h VI = 18.055 mis P= Power need to overcome the Drag A= frontal areas Cd I gv2 Con smooth pa Foov; For Drag force (4) Analysis of Boundary Layer *: Due to Bowdary Layer development there wa skin friction / Drag Cofficient (1) Defined as To St Density of fluid of medlem ikg/m3) Q Co + Depends upon Reynolds number (Reid) assume 848 face of :60 = f(Re) 64 Go = 0.316 Co = Rein (Rep) 14 Laminar Boundary turbulent Bound orgy layey Development dager Assume ReiD = SVP A Red = 1.23x 18055 x1 S = 1.23 kg/m3 4 1'81810-5 M=1181810-5 pas Dynmic uncosity > +5 ReiD = 12.33810-75x10 Dalm TURBULEHT FLOW

Foa V2 given condition is turbulent How to & (Red)/4 2 FD = Cox SAV? I FO = CO JAU? 12-14 a ult SVD1/4 2 a from Eq0 P = Fo.v 4 pa voula Ipaul14 > from Ea 0 and ② case you ty remain same paco P2 = CD2 CD) Pi lacu P2= Pitoys, Partners IP2= laspil ² Power A by gs). so in case the power required will increase by 25% It speed will remain same How power will reamain some P2 = 1 Pa CD XV EDIUI - CD 2 V2 V22 Gell. Vi > V2=0.80V, TIL PI V2 = 0.80V, - 52 kmh Cd

3 416) Q = fo els 5.06MB/s - G- Axu 0.06 Vda. Q 7. 64m/s d=0.1m (0:1) no= '70 P= 3 (power required by pump) Apply Bernaute's equation between D and Pi + V12 + 1 = 89 29 03 AL(S) = f L Vg² 290 P² + V2² + 2 thels) the (d) + vg2 - rij 29 28 Manometria Head l H2 : read ageinst which pump has to work Defined as H = hs that hus + hid) + ud ? -(1) 2g hs= suction head in cm Losses in suction pipe and ha= Dell very head in (m) Dellvery pipe head ALS) = he oss in suction pipe (m) Lossin Delivery poße (m) Vd = velouty head at Discharge polnt Delivery tenk veloursty. from the given fig ② hs = 4m hd = om Va?: 8.99m 29 0 head biasa 2 (2485 Length of suction albe and delivery pipe is missing Assume Losses in suchon any Delivery bripe =0 Ig ' SQgH no= from Eqciis P H= 6+4+2.97 = 12.97m Piaf еван = 1000x0.06x 9.81% 12.97 Por 7634.142 W Pided = 7.634 KW + Actual Power P= Pichael => [Peeted = 10.90 kW/ По

4 PLA PL+ .21= P + Pts 10:3-(2097+ 4) v4² 89 29 Pu Hatm 89 89 Now Apply Bernaulliis Equation at point o and ☺ that go + 22 + even Ve yt22 ( 4 +22) Hatm to to PL 89 R has a louction tead to avoid cave'tation ) Pi = 3.33m sy Pl= 32.66 kPa Now, Again apply Blean between M and ☺ cele in the up +2m) - (4 + zan) = Hon 2 Hm=8m pm=78.48 kPa Pm=78.48 KM/m2 PL= 32.66 kN/m2 2