Water enters a nozzle steadily at 3 kg/m^3 and 50 m/s and leaves at 2 kg/m^3 and 220 m/s. If the inlet area of the
nozzle is 100cm^2 , Determine:
a. Mass flow rate through the nozzle,
b. Exit area of the nozzle.
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a. To determine the mass flow rate through the nozzle, we can use the equation:
mass flow rate = density × velocity × area
Given that the density at the inlet is 3 kg/m^3, the velocity at the inlet is 50 m/s, and the inlet area is 100 cm^2 (or 0.01 m^2), we can substitute these values into the equation:
mass flow rate = 3 kg/m^3 × 50 m/s × 0.01 m^2
mass flow rate = 1.5 kg/s
Therefore, the mass flow rate through the nozzle is 1.5 kg/s.
b. To determine the exit area of the nozzle, we can use the equation:
mass flow rate = density × velocity × area
Given that the density at the outlet is 2 kg/m^3, the velocity at the outlet is 220 m/s, and the mass flow rate is 1.5 kg/s, we can rearrange the equation to solve for the exit area:
area = mass flow rate / (density × velocity)
area = 1.5 kg/s / (2 kg/m^3 × 220 m/s)
area ≈ 0.0034 m^2
Therefore, the exit area of the nozzle is approximately 0.0034 m^2.
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