Question

The open cylindrical tank in the figure contains water and is being filled as shown. Assume incompressible flow with pwater = 1000 kg/m^3.

1. (15 marks): The open cylindrical tank in the figure contains water and is being filled as shown. Assume incompressible flow, with water = 1000 kg/m3. a) Write the mass transport equation and note that the flow may not be steady, which implies that the rate of change of mass in the control volume needs not be 0 and is rather equal to the change of mass n Q=0.01 m/s the control volume (aka the bucket). b) Simplify the above equation and derive an analytical expression for the water level change dh/dt, in terms of the volume flow rates Q1, Q2 and Q3, and the tank diameter d; D = 5 cm c) If the water level stays constant (i.e., steady flow), determine the exit velocity V2 given V = 3 m/s and D, = 7 cm Q3 = 0.01 m/s. Water

Answer 1

Solution! - control volume, Di = 5cm - - - - - - - - prepare a dasa table: - Dasa value unit Q30 .01 i mis 3 mis Di 5 cm Dz 7 cm According to question Assumptions: incompressible flow = contand) 17 The tank and pipes have noross-section ay For control valume teak, Mass transfer equation is, circular 1 t ( Span) + 8 (92-8, 1992)=0 (1)

Hollome of termel = 72 h. + mout - min by put the value u in eam (1) ♡ Taldh It& (82-81-83) = 0 ? 4 Tot dth = Bit Q3-82 dd (ad2%) 1 If CSF & D AW, 92 = 8 0 2 2 A V2 48 93 803²A/3 them, dh Devi + Dog Vs - D22 V 2 do o d2

c) Find velocity Va, From the convereation 922 Bit 83 of mass, V er 1992 +93) 8 V2 = 4.13 mis a I Result, ay (Spau) + 8 (938, -4) - by dh a ltazQ2. dt. At c) 4.13 018