Answer to Question #123977 in Molecular Physics | Thermodynamics for Chidera

Question

A nozzle is a device for increasing the velocity of a steadily flowing stream of fluid. At the inlet to a certain nozzle the enthalpy of the fluid is 3025kj/kg and the velocity is 60m/s. At the exit from the nozzles the enthalpy is 2790kj/kg.The nozzle is horizontal and there is negligible heat loss from it.
(i) Find the velocity at the nozzle exit.
(ii) If the inlet area is 0.1m^2 and the specific volume at the inlet is 0.19m^3/kg. Find the rate of flow of fluid.
(ii) If the specific volume at the nozzle exit is 0.5m^3/kg. Find the exit area of the nozzle

Answer 1

i) According to Conservation Energy:

$$h_1+0.5v^2_1=h_2+0.5v^2_2$$

$$3000 .10^3+0.5(60)^2=2762.10^3+0.5v^2_2$$

$$v_2=692.5\frac{m}{s}$$

ii)Rate of flow of fluid:

$$\frac{dm}{dt}=\frac{dv}{dt}\frac{dv}{dm}$$

$$\frac{dv}{dt}=Av_1$$

$$\frac{dm}{dt}=\frac{60.0.1}{0.19}=31.6\frac{kg}{s}$$

ii) Exit area of nozzle;

$$\frac{dm}{dt}={v_2A'}\frac{dv}{dm}$$

$$31.6=\frac{692.5A'}{0.5}$$

$$A'=0.0228m^2$$