A horizontal air diffuser operates with inlet velocity and specific enthalpy of 250 m/s and 270.11 kj/kg, repectively, and exit specific enthalpy of 297.31 kj/kg. For negligible heat transfer with the surroundings, the exit velocity is

a) 223 m/s

b) 197 m/x

c) 90 m/s

d) 70 m/s

c) 90 m/s

Explanation:

Given

Invest velocity, v1 = 250 m/s

Inlet specific enthalpy, h1 = 270.11 kJ/kg = 270110 J/kg

Outlet specific enthalpy, h2 = 297.31 kJ/kg = 297310 J/kg

Outlet velocity, v2 = ?

0 = Q(cv) - W(cv) + m[(h1 - h2) + 1/2(v1² - v2²) + g(z1 - z2)]

0 = Q(cv) + m[(h1 - h2) + 1/2(v1² - v2²)]

0 = [(h1 - h2) + 1/2(v1² - v2²)]

Substituting the values of the above, we get

0 = [(270110 - 297310) + 1/2 ( 250² - v²)

0 = [-27200 + 1/2 (62500 - v²)]

27200 = 1/2 (62500 - v²)

54400 = 62500 - v²

v² = 62500 - 54400

v² = 8100

v = √8100

v = 90 m/s

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