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4vir4ik [10]
3 years ago
11

Air enters a 200 mm diameter adiabatic nozzle at 195 deg C, 500 kPa and 100 m/s. It exits at 85 kPa. If the exit diameter is 158

mm, what are the temperature and velocity at the exit?
Engineering
1 answer:
ahrayia [7]3 years ago
8 0

Answer:

v_2 = 160.23 m/s

T_2 = 475.797 k

Explanation:

given data:

Diameter =d_1 = 200mm

t_1 =195 degree

p_1 =500 kPa

v_1 = 100m/s

p_2 = 85kPa

d_2 = 158mm

from continuity equation

A_1v_1 = A_2v_2

v_2 = \frac{\frac{\pi}{4}d_1^2 v_1^2}{\frac{\pi}{4}d_2^2}

v_2 = \frac{d_2v_1}{d_2^2}

v_2 = [\frac{d_1}{d_2}]^2 v_1

      = [\frac{0.200}{0.158}]^2 \times 100

v_2 = 160.23 m/s

by energy flow equation

h_1 + \frac{v_1^2}{2} +gz_1 +q =h_2 + \frac{v_2^2}{2} +gz_2 +w

z_1 =z_2 and q =0, w =0 for nozzle

therefore we have

h_1 -h_2 =\frac{v_1^2}{2} -\frac{v_2^2}{2}

dh = \frac{1}{2} (v_1^2 -v_2^2)

but we know dh = Cp dt

hence our equation become

Cp(T_2 -T_1) = \frac{1}{2} (v_1^2 -v_2^2)

Cp (T_2 -T_1) = 7836.94

(T_2 -T_1) = \frac{7836.94}{1.005*10^3}

(T_2 -T_1) = 7.797

T_2 = 7.797 +468 = 475.797 k

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