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Iii Mechanical
mechanical engineering question- how would i approach this question?
b)A nozzle is a device for increasing the velocity of a steadily flowing fluid. At the inlet to a certain nozzle the specific enthalpy of the fluids is 3025 kJ/kg and the velocity is 60 m/s. At the exit from the nozzle the specific enthalpy is
2790 kJ/kg. The nozzle is horizontal and there is a negligible heat loss from it. Calculate:
i)the velocity of the fluid at exit;
(6 marks)
ii)the rate of the flow of fluid when the inlet area is 0.1 m2 and the specific volume at the inlet is 0.19 m3/kg;
(4 marks)
iii)the exit area of the nozzle when the specific volume at the nozzle exit is 0.5m3/kg.
(3 marks)
Background: a nozzle converts Pressure energy into velocity energy.
Pressure energy is in the form of enthalpy, velocity energy is in the form of kinetic energy.
for an adiabatic, isentropic nozzle, the steady energy flow equation reduces to
m_dot*(h1 + v1^2/2) = m_dot*(h2 + v2^2/2)
i)
re-arrange for v2:
v2^2/2 = h1 – h2 + v1^2/2
v2 = sqrt(2*(h1-h2) + v1^2)
convert enthalpies to J/kg in order to use this formula.
ii)
Mass flow rate is geometrically related to velocity as such
m_dot = rho*v*A_x-sect
Definition of specific volume
rho = 1/specvol
result:
m_dot = v1*A1/specvol_1
iii)
Use conservation of mass, and same geometric relation
m_dot = v2*A2/specvol_2
re-arrange for area:
A2 = m_dot*specvol_2/v2
