Question

9Im 100 s- 1500 rpm 80 70 60 R1 PI R2 Pa 30 Im 10 Pa 0 0.515 25 3 35 3) [20 pts.J A pump given by the characteristic curve is used in the process shown above. The fluid with density of p 1019 kg/m3 filled by a hydrostatic my-10 kg/min flow rate. Laminar valve resistances are R-400 N min/kg m2 and R2 600 N -min/kg m2, tank area A a) Find the hydrostatic pressure and flow rate of the pump and determine the nominal operating point on the load line b) About the operating point derive an AC equivalent pump model and then the dynamic model valid for small variations 0.1 m2

Answer 1

Therefore density of fluid e = 1019 k g/m^3 flow rate q_m_1 = 10 k g/min R_1 = 400 N min/k g m^2 R_2 = 600 N min/k g m^2 A = 0.1 m^2 (a) hydrostatic pressure determined from a control volume analysis of infinitesimally small cube of Fluid therefore Pressure is force/Area p (z) - p (z_o) = 1/A integral^z_z_0 dz' doubleintegral_A dx' dy' e (z') g (z') = (integral^z_z_o dz' e (z') \r\n therefore e is fluid density p is the hydrostatic pressure g = 9.8 m/s^2 z_o = zero reference point pressure therefore p - p_o = e g h p = e g H + p (h) = p (o) e^-M g h/k T (b) for operating point therefore AC input impedance r_in = R_1 Vertical-bar Vertical-bar R_2 Vertical-bar Vertical-bar r_b_e r_in